Appointments shall be for a term of three years or until successors are appointed. Terms of office shall begin on the first day of the calendar year. Any vacancy shall be filled for the remainder of the unexpired term as provided in BC 2.03.192. The mayor, with the approval of the council, may remove any member of the board for cause. Members of the board holding office at the time of enactment of this code chapter shall hold office for the terms for which they were appointed and until their successors are appointed.