R.I. Gen. Laws § 8-13-2: Appointment of members — Vacancies.

In the month of January in each year, the governor shall appoint two (2) persons, qualified as provided in § 8-13-1, to succeed the members of the council whose offices shall next expire, to hold office for three (3) years and until their respective successors shall be appointed and qualified. Any vacancy that shall occur in the membership of the council shall be filled by another appointment by the governor for the remainder of the term.