(a) When any local or general law authorizes or requires the remaining members of the governing body of a political subdivision of this state to appoint a person to fill a vacancy occurring in that body, the absence of a quorum caused by any such vacancy or vacancies shall not impair the authority of a majority of the remaining members of such body to make that appointment.(b) When any local or general law provides for the appointment, other than appointment by the Governor, of a person to fill a vacancy in an elective public office and such vacancy is not filled within 45 days after the vacancy occurs, the Governor shall appoint a person to fill such vacancy. A person appointed by the Governor to fill a vacancy pursuant to this subsection shall serve until such time as that person would serve had the person been appointed as provided in that local or general law.
Georgia Legal Code