Exhibit 10.1

10 Cabot Place, Stoughton, MA 02072

June 30, 2016

Mr. James P. McDonough

81 Hannah Niles Way

Braintree, MA 02184

Dear Jim,

In connection with the conversion of Randolph Bancorp from a mutual holding company to a stock holding company structure, it is necessary to make certain technical changes to the terms of the letter agreement dated March 22, 2013 among you, Randolph Bancorp and Randolph Savings Bank (the “Letter Agreement”). Section 15 of the Letter Agreement provides that it may be modified by a written agreement signed by you and the Board.

Effective June 30, 2016, Section 10 of the Letter Agreement is hereby amended by adding the following sentence at the end thereof:

“Anything in this letter agreement to the contrary notwithstanding, if at the time of your “separation from service” within the meaning of Section 409A of the Code, the Bank determines that you are a “specified employee” within the meaning of Section 409A(a)(2)(B)(i) of the Code, then to the extent any payment or benefit that you become entitled to under this letter agreement on account of your separation from service would be considered deferred compensation subject to the 20 percent additional tax imposed pursuant to Section 409A(a) of the Code as a result of the application of Section 409A(a)(2)(B)(i) of the Code, such payment shall not be payable and such benefit shall not be provided until the date that is the earlier of (A) six months and one day after your separation from service, or (B) your death.”

Please indicate your acceptance of the foregoing amendment by your signature below.

877-963-2100  •  www.randolphsavingsbank.com