Exhibit 5.1

​ ​	​ Houston, Texas 77002-2929 ​ 713 • 220 • 4200 Fax713 • 220 • 4285 ​ ​
​ ​	Hunton Andrews Kurth LLP 600 Travis, Suite 4200 Houston, Texas 77002-2929 ​ Tel713 • 220 • 4200 Fax713 • 220 • 4285 ​

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September 17, 2021

Evolve Transition Infrastructure LP

1360 Post Oak Blvd.

Suite 2400

Houston, Texas 77056

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Re: Common Units to be issued by Evolve Transition Infrastructure LP.

Ladies and Gentlemen:

We have acted as counsel to Evolve Transition Infrastructure LP, a Delaware limited partnership (the “Partnership”), in connection with the offering and sale, from time to time, by the Partnership of common units representing limited partner interests in the Partnership (the “Common Units”). Such offering and sale have been registered with the United States Securities and Exchange Commission (the “SEC”), pursuant to the Partnership’s registration statement on Form S-3 (File No. 333-254509) filed with the SEC on March 19, 2021. Such registration statement, at the time it was declared effective by the SEC on March 31, 2021, is referred to herein as the “Registration Statement.”

The Partnership plans to conduct such offering of Common Units having an aggregate offering price of up to $1,652,500, pursuant to (i) its prospectus dated March 31, 2021 (the “Prospectus”) included in the Registration Statement, as supplemented by its prospectus supplement dated September 17, 2021 (the “Prospectus Supplement”) filed with the SEC on September 17, 2021 and (ii) the ATM Sales Agreement dated April 20, 2021 (the “Sales Agreement”) between the Partnership and Virtu Americas LLC (the “Agent”). Pursuant to the Sales Agreement, the Partnership plans to issue and sell Common Units (i) through the Agent as sales agent or (ii) to the Agent as principal. The Common Units to be issued and sold pursuant to the Sales Agreement are referred to herein as the “Securities.”

In rendering the opinions set forth herein, we have read and examined and relied on originals or copies, certified or otherwise identified to our satisfaction, of such documents and records of the Partnership and Evolve Transition Infrastructure GP LLC, a Delaware limited liability company and the general partner of the Partnership (the “General Partner”), certificates of public officials, certificates and statements of officers of the General Partner, and such other documents, certificates and records as we have deemed necessary to render the opinions set forth herein, including, among other things: (i) the Certificate of Limited Partnership of the Partnership, as amended (the “Partnership Certificate”), (ii) the Third Amended and Restated Agreement of Limited Partnership of the Partnership, as amended (the “Partnership

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Evolve Transition Infrastructure LP

September 17, 2021

Page 2

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Agreement”); (iii) the Certificate of Formation of the General Partner, as amended (the “GP Certificate”), (iv) the Limited Liability Company Agreement of the General Partner, as amended (the “GP LLC Agreement”), and (v) certain resolutions of the Board of Directors of the General Partner. In our examination, we have assumed, without independent investigation, (a) the genuineness of the signatures on all documents that we have examined, (b) the legal capacity of all natural persons, (c) the authenticity of all documents supplied to us as originals, (d) the conformity to the authentic originals of all documents supplied to us as certified, photostatic, electronic or otherwise reproduced copies, and (e) the authenticity of the originals of such latter documents. As to any facts material to the opinions expressed herein that we did not independently establish or verify, we have relied, to the extent we deem appropriate, upon (i) oral or written statements and representations of officers and other representatives of the General Partner and (ii) statements and certifications of public officials and others.

We have also assumed that, at the time of issuance, sale and delivery of any of the Securities, the Partnership Certificate, the Partnership Agreement, the GP Certificate and the GP LLC Agreement, in each case as amended to date, will not have been amended in any manner that would affect any legal conclusion set forth herein.

Our opinions expressed herein are limited to the Delaware Revised Uniform Limited Partnership Act and the Delaware Limited Liability Company Act, and we express no opinion as to the laws of any other jurisdiction.

Based upon the foregoing and subject to the limitations, qualifications, exceptions and assumptions set forth herein, we are of the opinion that when any of the Securities have been issued and delivered against payment therefor in accordance with the terms of the Sales Agreement, (a) such Securities will be validly issued and (b) purchasers of such Securities will have no obligation, solely by reason of their ownership of such Securities, to make any contributions to the Partnership or any further payments for their purchase of such Securities, and such purchasers will have no personal liability, solely by reason of their ownership of such Securities, to creditors of the Partnership for any of its debts, liabilities or other obligations.

We consent to the filing by you of this opinion as an exhibit to the Partnership’s Current Report on Form 8-K filed with the SEC on the date hereof, and we further consent to the use of our name under the caption “Legal Matters” in the Prospectus and under the caption “Legal Matters” in the Prospectus Supplement. In giving this consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the SEC. This opinion is expressed as of the date hereof, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in law.

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