On the death, removal, resignation, change of residence to a place outside the county, or inability to act as a member of the library board, a vacancy on the library board shall exist and such vacancy shall be filled by appointment by the mayor of the city and chairman of the board of county commissioners, acting jointly, and with the approval of the city commission and the board of county commissioners, to fill the unexpired term of such member. (Prior code § 11A-7).