R.I. Gen. Laws § 42-16.1-8: Filling of vacancies on board.

In case there is a vacancy in the board of review while the senate is in session, the governor shall appoint in the manner aforesaid. In case there is a vacancy in the board of review when the senate is not in session, the governor shall appoint some person to hold office until the next session thereof. Vacancies shall be filled in such manner that the representation of labor, industry, and the public shall at all times be retained on the board of review.