Utah Code § 9-7-403: Library board terms -- Officers -- Removal -- Vacancies.

(1) Each director of a library board shall be appointed for a three-year term, or until the successor to that director is appointed. Initially, appointments shall be made for one-, two-, and three-year terms. Annually thereafter, the city governing body shall, before the first day of July of each year, appoint for a three-year term directors to take the place of the retiring directors.

(2) Directors shall serve not more than two consecutive full terms.

(3) The directors shall annually select a chairman and other officers.

(4) The city governing body may remove any director for misconduct or neglect of duty.

(5) Vacancies in a library board of directors shall be filled for the unexpired term in the same manner as original appointments.