Exhibit 1.2

OPPENHEIMER & CO., INC.

85 Broad Street, 23^rd Floor

New York, New York 10004

EARLYBIRDCAPITAL, INC.

366 Madison Avenue

New York, New York 10017

            , 2018

Pure Acquisition Corp.

c/o HighPeak Pure Acquisition, LLC

421 W. 3^rd Street, Suite 1000

Fort Worth, Texas 76102

Attn: Jack D. Hightower, Chief Executive Officer

Ladies and Gentlemen:

This is to confirm our agreement whereby Pure Acquisition Corp., a Delaware corporation (“Company”), has requested Oppenheimer & Co., Inc. and EarlyBirdCapital, Inc. (each, an “Advisor” and together the “Advisors”) to assist it in connection with the Company merging with, acquiring, engaging in a share exchange, share recapitalization, reorganization, purchasing all or substantially all of the assets of, entering into contractual arrangements, or engaging in any other similar business combination (in each case, a “Business Combination”) with one or more businesses or entities (each a “Target”) as described in the Company’s Registration Statement on Form S-1 (File No. 333-223845) filed with the Securities and Exchange Commission (“Registration Statement”) in connection with its initial public offering (“IPO”).

Notwithstanding anything to the contrary contained herein, the Services to be provided for hereunder will not include any solicitation of potential investors in connection with the IPO; provided; however, as set forth in Section 8 of the Underwriting Agreement entered into between the Company, Oppenheimer & Co., Inc. and EarlyBirdCapital, Inc. in connection with the IPO (the “Underwriting Agreement”), the Company may be entitled to terminate this Agreement with respect to one or more of the Advisors under certain circumstances set forth therein in connection with the IPO.

(b)    As compensation for the Services, the Company will pay the Advisors a cash fee equal to, in the aggregate, 3.5% of the gross proceeds received by the Company in the IPO (“Fee”). The Advisor’s portion of the Fee is due and payable to the Advisors by wire transfer at the closing of the initial Business Combination (“Closing”), and shall be allocated evenly between the Advisors. If a proposed Business Combination is not consummated for any reason, no Fee shall be due or payable to the Advisors hereunder. The Fee shall be exclusive of any other fees which may become payable to the Advisors pursuant to any other agreement between the Advisors and the Company or the Target.

The Company will provide full cooperation to each Advisor as may be necessary for the efficient performance by such Advisor of its obligations hereunder, including, but not limited to, providing to such Advisor and its counsel, on a timely basis, all documents and information regarding the Company and Target that such Advisor may reasonably request or that are otherwise relevant to the Advisor’s performance of its obligations hereunder (collectively, the “Information”); making the Company’s management, auditors, suppliers, customers, consultants and advisors available to each Advisor; and, using commercially reasonable efforts to provide each Advisor with reasonable access to the management, auditors, suppliers, customers, consultants and advisors of Target. The Company will promptly notify each Advisor of any change in facts or circumstances or new developments affecting the Company or Target or that might reasonably be considered material to any Advisor’s engagement hereunder.

The Company represents, warrants and covenants to each Advisor that all Information it makes available to the Advisor by or on behalf of the Company in connection with the performance of its obligations hereunder will not contain any untrue statement of a material fact or omit to state a material fact necessary in order to make statements made, in light of the circumstances under which they were made, not misleading as of the date thereof and as of the consummation of the Business Combination.

The Company shall indemnify the Advisors and their affiliates and directors, officers, employees, shareholders, representatives and agents in accordance with the indemnification provisions set forth in Annex I hereto, all of which are incorporated herein by reference.

[Signature Page to Business Combination Marketing Agreement]

Notwithstanding the foregoing and Annex 1, each Advisor agrees, if there is no Closing, (i) that it does not have any right, title, interest or claim of any kind in or to any monies in the Company’s trust account (“Trust Account”) established in connection with the IPO with respect to the Fee (each, a “Claim”); (ii) to waive any Claim it may have in the future as a result of, or arising out of, any services provided to the Company hereunder; and (iii) to not seek recourse against the Trust Account with respect to the Fee.

Without any Advisor’s prior written consent, neither the Company nor any of its affiliates (nor any director, officer, manager, partner, member, employee or agent thereof) shall quote or refer to (i) such Advisor’s name or (ii) any advice rendered by such Advisor to the Company or any communication from such Advisor in connection with performance of its services hereunder, except as required by applicable federal or state law, regulation or securities exchange rule.

Each Advisor shall perform the Services as an independent contractor and not as an employee of the Company or affiliate thereof. It is expressly understood and agreed to by the parties that no Advisor shall have authority to act for, represent or bind the Company or any affiliate thereof in any manner, except as may be expressly agreed to by the Company in writing. In rendering such services, each Advisor will be acting solely pursuant to a contractual relationship on an arm’s-length basis. This Agreement is not intended to create a fiduciary relationship between the parties and neither any Advisor nor any of such Advisor’s officers, directors or personnel will owe any fiduciary duty to the Company or any other person in connection with any of the matters contemplated by this Agreement.

The Company acknowledges that the Advisors are full-service securities firms engaged in securities trading and brokerage activities and providing investment banking and advisory services from which conflicting interests may arise. In the ordinary course of business, the Advisors and their affiliates may at any time hold long or short positions, and may trade or otherwise effect transactions, for their own account or the accounts of customers, in debt or equity securities of the Company, its affiliates or other entities that may be involved in the transactions contemplated hereby. Nothing in this Agreement shall be construed to limit or restrict any Advisor or any of its affiliates in conducting such business.

This Agreement and the Underwriting Agreement constitute the entire understanding between the parties with respect to the subject matter hereof and supersedes all prior agreements and understandings, oral or written, with respect thereto. This Agreement may not be modified or terminated orally or in any manner other than by an agreement in writing signed by the parties hereto.

[Signature Page to Business Combination Marketing Agreement]

Any notices required or permitted to be given hereunder shall be in writing and shall be deemed given when mailed by certified mail or private courier service, return receipt requested, addressed to each party at its respective addresses set forth above, or such other address as may be given by a party in a notice given pursuant to this Section.

This Agreement may not be assigned by any party without the written consent of the other parties hereto. This Agreement shall be binding upon and shall inure to the benefit of the parties hereto and, except where prohibited, to their successors and assigns.

Nothing herein shall be deemed to restrict or prohibit the engagement by the Company of other consultants providing the same or similar services or the payment by the Company of fees to such parties. The Company’s engagement of any other consultant(s) shall not affect any Advisor’s right to receive its portion of the Fee, pursuant to this Agreement.

This Agreement shall be construed and enforced in accordance with the laws of the State of New York without giving effect to conflict of laws.

In the event of any dispute under this Agreement, then and in such event, each party hereto agrees that the dispute shall be brought and enforced in the courts of the State of New York, County of New York under the accelerated adjudication procedures of the Commercial Division, or the United States District Court for the Southern District of New York, in each event at the discretion of the party initiating the dispute. Each party irrevocably submits to such jurisdiction, which jurisdiction shall be exclusive. Each party waives any right to a jury trial in respect of any such dispute. Each party hereby waives any objection to such exclusive jurisdiction and that such courts represent an inconvenient forum. Any such process or summons to be served upon a party may be served by transmitting a copy thereof by registered or certified mail, postage prepaid, addressed to such party at the address set forth at the beginning of this Agreement. Such mailing shall be deemed personal service and shall be legal and binding upon the party being served in any action, proceeding or claim. The parties agree that the prevailing party(ies) in any such action shall be entitled to recover from the other party(ies) all of its reasonable attorneys’ fees and expenses relating to such action or proceeding and/or incurred in connection with the preparation therefor.

This Agreement may be executed in several original or facsimile counterparts, each one of which shall constitute an original, and together shall constitute but one instrument.

[Signature Page to Business Combination Marketing Agreement]

If the foregoing correctly sets forth the understanding between the Advisors and the Company with respect to the foregoing, please so indicate your agreement by signing in the place provided below, at which time this letter shall become a binding contract.

[Signature Page to Business Combination Marketing Agreement]

ANNEX I

Indemnification

In connection with the Company’s engagement of Oppenheimer & Co., Inc. and EarlyBirdCapital, Inc. (each, an “Advisor” and together the “Advisors”) pursuant to that certain letter agreement (“Agreement”) of which this Annex forms a part, Pure Acquisition Corp. (the “Company”) hereby agrees, subject to the second paragraph of Section 4 of the Agreement, to indemnify and hold harmless each Advisor and its affiliates and its respective directors, officers, shareholders, agents and employees of any of the foregoing (collectively the “Indemnified Persons”), from and against any and all claims, actions, suits, proceedings (including those of stockholders), damages, liabilities and expenses incurred by any of them (including the reasonable fees and expenses of counsel), as incurred, (collectively a “Claim”), that (A) are related to or arise out of (i) any actions taken or omitted to be taken (including any untrue statements made or any statements omitted to be made) by the Company, or (ii) any actions taken or omitted to be taken by any Indemnified Person in connection with the Company’s engagement of the Advisors, or (B) otherwise relate to or arise out of any Advisor’s activities on the Company’s behalf under such Advisor’s engagement, and the Company shall reimburse any Indemnified Person for all expenses (including the reasonable fees and expenses of counsel) as incurred by such Indemnified Person in connection with investigating, preparing or defending any such claim, action, suit or proceeding, whether or not in connection with pending or threatened litigation in which any Indemnified Person is a party. The Company will not, however, be responsible for any Claim that is finally judicially determined to have resulted primarily from the bad faith, gross negligence or willful misconduct of any person seeking indemnification for such Claim. The Company further agrees that no Indemnified Person shall have any liability to the Company for or in connection with the Company’s engagement of the Advisors except for any Claim that is finally judicially determined to have resulted primarily from such Indemnified Person’s bad faith, gross negligence or willful misconduct.

The Company further agrees that it will not, without the prior written consent of any Advisor, settle, compromise or consent to the entry of any judgment in any pending or threatened Claim in respect of which indemnification may be sought hereunder (whether or not any Indemnified Person is an actual or potential party to such Claim), unless such settlement, compromise or consent includes an unconditional, irrevocable release of each Indemnified Person from any and all liability arising out of such Claim.

Promptly upon receipt by an Indemnified Person of notice of any complaint or the assertion or institution of any Claim with respect to which indemnification is being sought hereunder, such Indemnified Person shall notify the Company in writing of such complaint or of such assertion or institution but failure to so notify the Company shall not relieve the Company from any obligation it may have hereunder, except and only to the extent such failure results in the forfeiture by the Company of substantial rights and defenses. If the Company so elects or is requested by such Indemnified Person, the Company will assume the defense of such Claim, including the employment of counsel reasonably satisfactory to such Indemnified Person and the payment of the fees and expenses of such counsel. In the event, however, that legal counsel to such Indemnified Person reasonably determines that having common counsel would present such counsel with a conflict of interest or if the defendant in, or target of, any such Claim, includes an Indemnified Person and the Company, and legal counsel to such Indemnified Person reasonably

Annex 1 – 1

concludes that there may be legal defenses available to it or other Indemnified Persons different from or in addition to those available to the Company, then such Indemnified Person may employ its own separate counsel to represent or defend him, her or it in any such Claim and the Company shall pay the reasonable fees and expenses of such counsel. Notwithstanding anything herein to the contrary, if the Company fails timely or diligently to defend, contest, or otherwise protect against any Claim, the relevant Indemnified Party shall have the right, but not the obligation, to defend, contest, compromise, settle, assert crossclaims, or counterclaims or otherwise protect against the same, and shall be fully indemnified by the Company therefor, including without limitation, for the reasonable fees and expenses of its counsel and all amounts paid as a result of such Claim or the compromise or settlement thereof.

In addition, with respect to any Claim in which the Company assumes the defense, the Indemnified Person shall have the right to participate in such Claim and to retain his, her or its own counsel therefor at his, her or its own expense.

The Company agrees that if any indemnity sought by an Indemnified Person hereunder is held by a court to be unavailable or insufficient for any reason then (whether or not any Advisor is an Indemnified Person), the Company and such Advisor shall contribute to the Claim or portion thereof for which such indemnity is held unavailable or insufficient in such proportion as is appropriate to reflect the relative benefits to the Company, on the one hand, and such Advisor on the other, in connection with such Advisor’s engagement referred to above, subject to the limitation that in no event shall the amount of any Advisor’s contribution to such Claim exceed the amount of fees actually received by such Advisor from the Company pursuant to such Advisor’s engagement. The Company hereby agrees that the relative benefits to the Company, on the one hand, and the Advisors on the other, with respect to the Advisors’ engagement shall be deemed to be in the same proportion as (a) the total value paid or proposed to be paid or received by the Company or its stockholders as the case may be, pursuant to the transaction (whether or not consummated) for which the Advisors are engaged to render services bears to (b) the fee paid or proposed to be paid to the Advisors in connection with such engagement.

The Company’s indemnity, reimbursement and contribution obligations under this Agreement (a) shall be in addition to, and shall in no way limit or otherwise adversely affect any rights that any Indemnified Party may have at law or at equity and (b) shall be effective whether or not the Company is at fault in any way.

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