Georgia Code Title 21. Elections § 21-2-504

(a) Whenever any primary or election shall fail to fill a particular nomination or office and such failure cannot be cured by a run-off primary or election, whenever any person elected to public office shall die or withdraw prior to taking office, or whenever any person elected to public office shall fail to take that office validly, the authority with whom the candidates for such nomination or office file notice of candidacy shall call a special primary or election to fill such position. If a special primary will not be held and unless otherwise provided by law, the call of a special election shall be made within 45 days after the occurrence of the vacancy.

(b) Whenever any person elected to municipal public office shall, after taking office, die, withdraw, or for any other reason create a vacancy in his or her office and the municipal charter fails to provide a method for the filling of such vacancy, the governing authority shall thereupon call a special election to fill such vacancy.