Tenn. Code Ann. § 16-18-204

A vacancy in the office of the popularly elected city judge shall be filled by appointment by the governing body. The person appointed, however, may serve only until the next regular August general state election. At this election, a person shall be elected to serve any unexpired term if the full term is not to be filled at the election. In the temporary absence or inability of the city judge, the governing body shall appoint a qualified person to serve until the judge's return.