Exhibit 5.1

December 7, 2023

Arrow Financial Corporation

250 Glen Street

Glens Falls, NY 12801

Re: Registration Statement on Form S-8 for seventy-five thousand (75,000) shares of Arrow Financial Corporation Common Stock, par value $1.00, for issuance to participants under the Arrow Financial Corporation 2023 Directors’ Stock Plan

Ladies and Gentlemen:

We have served as counsel to Arrow Financial Corporation, Glens Falls, New York (the “Company”), in connection with the preparation and filing of a registration statement (and included prospectus) on Form S-8 (the “Registration Statement”) under the Securities Act of 1933, as amended, and the Rules and Regulations promulgated thereunder (the “Securities Act”), registering the offer and sale by the Company of up to seventy-five thousand (75,000) shares of common stock of the Company, par value $1.00 per share (the “Shares”), through the Arrow Financial Corporation 2023 Directors’ Stock Plan (the “Plan”).

We have examined such corporate records of the Company, such laws and such other information as we have deemed relevant, including the Company’s Certificate of Incorporation and all amendments thereto, By-laws and all amendments thereto and statements we have received from officers and representatives of the Company. In delivering this opinion, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as certified, photostatic or conformed copies, the authenticity of originals of all such latter documents, and the correctness of statements submitted to us by officers and representatives of the Company. Except to the extent expressly set forth herein, we have not undertaken any independent investigation to determine the existence or absence of such facts and no inference as to our knowledge of the existence or absence of such facts should be drawn from our representation of the Company.

Based solely on the foregoing, we are of the opinion that the Shares to be issued by the Company have been duly authorized and, when issued and sold by the Company in accordance with the Plan, will be legally issued, fully paid and non-assessable.

We hereby consent to the filing of this opinion as an Exhibit to the Registration Statement.

Our opinions set forth above are limited to the Federal laws of the United States of America and the laws of the State of New York.

This opinion may only be used, quoted or relied upon for the purpose of complying with the Securities Act in connection with the filing of the Registration Statement and may not be furnished to, quoted to or relied upon by any other person or entity for any purpose, without our prior written consent. Please note that we are opining only as to the matters expressly set forth herein and no opinion should be inferred as to any other matters. No opinion is expressed herein with respect to the qualification of the Shares under the securities or blue sky laws of any state or any foreign jurisdiction.

Very truly yours,

/s/ THOMPSON COBURN LLP