Exhibit 5.1

November 10, 2021

Evolve Transition Infrastructure LP

1360 Post Oak Blvd

Suite 2400

Houston, Texas 77056

Re: Common Units of Evolve Transition Infrastructure LP.

Ladies and Gentlemen:

We have acted as special counsel to Evolve Transition Infrastructure LP, a Delaware limited partnership (the “Partnership”), in connection with the preparation of a registration statement on Form S-1 (the “Registration Statement”) filed with the U.S. Securities and Exchange Commission (the “SEC”) on November 10, 2021 pursuant to the Securities Act of 1933, as amended (the “Securities Act”). The Registration Statement relates to the offering for resale from time to time, as set forth in the Registration Statement, the form of prospectus contained therein (the “Prospectus”) and one or more supplements to the Prospectus, by the selling unitholder named therein of up to 9,000,000 common units representing limited partner interests in the Partnership (“Common Units”) on terms to be determined at the time of the offering thereof.

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 Agreement”); (iii) the Certificate of Formation of the General Partner, as amended (the “GP Certificate”); and (iv) the Limited Liability Company Agreement of the General Partner, as amended (the “GP LLC Agreement”). 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.

ATLANTA AUSTIN BANGKOK BEIJING BOSTON BRUSSELS CHARLOTTE DALLAS DUBAI HOUSTON LONDON

LOS ANGELES MIAMI NEW YORK NORFOLK RICHMOND SAN FRANCISCO THE WOODLANDS TYSONS WASHINGTON, DC

www.HuntonAK.com

Evolve Transition Infrastructure LP

November 10, 2021

Page 2

We have also assumed that, at the time of resale and delivery of any of the Common Units being offered, 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 (a) the Common Units are validly issued, and (b) purchasers of such Common Units will have no obligation, solely by reason of their ownership of such Common Units, to make any contributions to the Partnership or any further payments for their purchase of such Common Units, and such purchasers will have no personal liability, solely by reason of their ownership of such Common Units, 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 Registration Statement and to the reference to this firm under the heading “Legal Matters” in the Prospectus. 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 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.