According to Sec. 3.09 of the Alabama Mayor-Council Act:

Vacancies in the council shall be filled by the council at the next regular meeting or any subsequent meeting of the council, the person so elected to hold office only until the next election of any kind in which the voters of the city to which this Act applies are qualified electors, at which time said unexpired terms shall be filled by said electors in accordance with all provisions of law applicable to such city; in any event, the person elected shall hold office until his successor is elected and qualified.