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Exhibit 1.3

May 12, 2015

Board of Trustees

Provident Bancorp

Boards of Directors

Provident Bancorp, Inc.

The Provident Bank

Five Market Street

Amesbury, MA 01913

Ladies and Gentlemen:

Reference is made to the letter agreement dated November 4, 2014 between Sandler O’Neill & Partners, L.P (“Sandler O’Neill”) and Provident Bancorp (the “MHC”), Provident Bancorp, Inc. (the “Bancorp”) and The Provident Bank (the “Bank”, and collectively with the MHC and the Bancorp, the “Company”), pursuant to which Sandler O’Neill agreed to act as exclusive marketing agent for the Company in connection with the offer and sale of certain shares of the common stock of the Bancorp (the “Marketing Agent Engagement Letter”).

The second and third sentences of the third paragraph of the “Subscription and Community Offering Fees” section are hereby deleted and the following inserted in lieu thereof:

“In recognition of the long lead times involved in the stock offering process, the Company agrees to make an advance payment to Sandler O’Neill in the amount of $25,000, payable upon execution of this letter, which shall be credited against any out-of-pocket accountable expenses payable hereunder. In the event that the advance exceeds the amount due in payment of out-of-pocket accountable, bona fide expenses actually incurred by Sandler O’Neill, the excess shall be refunded to the Company.”

Except as modified hereby, the terms and conditions of the Marketing Agent Engagement Letter shall remain in full force and effect.

Please confirm that the foregoing correctly sets forth our agreement by signing and returning to Sandler O’Neill the duplicate copy of this letter enclosed herewith.

[Signature Page Follows]

Accepted and agreed to as of

the date first above written:

provident Bancorp

provident Bancorp inc.

The provident bank

May 12, 2015

Board of Trustees

Provident Bancorp

Boards of Directors

Provident Bancorp, Inc.

The Provident Bank

Five Market Street

Amesbury, MA 01913

Ladies and Gentlemen:

Reference is made to the letter agreement dated November 4, 2014 between Sandler O’Neill & Partners, L.P (“Sandler O’Neill”) and Provident Bancorp (the “MHC”), Provident Bancorp, Inc. (the “Bancorp”) and The Provident Bank (the “Bank”, and collectively with the MHC and the Bancorp, the “Company”), pursuant to which Sandler O’Neill agreed to act as records management agent for the Company in connection with the offer and sale of certain shares of the common stock of the Bancorp (the “Records Agent Engagement Letter”).

The last paragraph of the “Servicer and fees” section is hereby deleted and the following inserted in lieu thereof:

“All fees under this agreement shall be due and payable in cash upon mailing of the offering materials.”

The “Costs and Expenses” section is hereby amended by adding the following new paragraph after the sole paragraph thereof:

“The Company agrees to make an advance payment against out-of-pocket accountable expenses in the amount of $25,000 payable in cash as follows: (a) $10,000 payable upon execution of this agreement and (b) the balance upon the mailing of the offering materials, all of which shall be credited against reimbursement of expenses payable hereunder and subject to the $30,000 maximum set forth in the preceding paragraph. In the event that the amount advanced by the Company hereunder exceeds the amount of reasonable out-of-pocket accountable, bona fide expenses actually incurred by Sandler O’Neill, the excess shall be refunded to the Company.”

Except as modified hereby, the terms and conditions of the Records Agent Engagement Letter shall remain in full force and effect.

Please confirm that the foregoing correctly sets forth our agreement by signing and returning to Sandler O’Neill the duplicate copy of this letter enclosed herewith.

[Signature Page Follows]

Accepted and agreed to as of

the date first above written:

provident Bancorp

provident Bancorp inc.

The provident bank