Utah Code § 17-37-3
Directors shall be appointed for three year terms, or until their successors are appointed. Initially, appointments shall be made for one, two, and three year terms. Annually thereafter, the county executive, with the advice and consent of the county legislative 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. Directors shall serve not more than two full terms in succession. Following such appointments, the directors shall meet and select a chairman and such other officers, as they deem necessary, for one-year terms. The county executive may remove any director for misconduct or neglect of duty. Vacancies in the board of directors, occasioned by removals, resignations, or otherwise, shall be filled for the unexpired terms in the same manner as original appointments.
Utah Code § 17-37-3