A tree warden whose appointment is approved by the director of environmental management holds office until the first day of March in the year following his or her appointment and until his or her successor is appointed and approved as provided in § 2-14-2. Any vacancy that may occur in the office of the tree warden of any city or town, from any cause, shall be filled by the town council of the town or by the mayor of any city, as the case may be, by the appointment of some person to serve as tree warden for the remainder of the term, and the appointment is subject to the approval of the director. If the town council of any town, or the mayor of any city, fails within sixty (60) days to appoint a tree warden as required by § 2-14-2 and this section, the director shall appoint some resident of the town or city to act as tree warden until an appointment is made by the town council or the mayor, as the case may be, and approved by the director as provided in § 2-14-2.