Tennessee Code Title 6. Cities and Towns § 6-53-106

(a) Notwithstanding any other law or municipal charter, whenever a vacancy occurs in the membership of any city board of education whose members are elected by vote of the people or in the office of city judge who is elected by vote of the people in any city having a population in excess of one hundred thousand (100,000) within counties, except those counties with the metropolitan form of government, having a population in excess of two hundred thousand (200,000), each according to the 1970 federal census or any subsequent federal census, any appointment made pursuant to law or charter provision shall be an interim appointment, valid only until the next primary or general election or referendum that is held in such city after the vacancy occurs.

(b) At such primary or general election or referendum, the vacancy shall be filled for the remainder of the unexpired term by the election of some qualified candidate.

(c) In any city to which this section applies, for those offices for which by charter or other law a special election is provided for the filling of vacancies, such charter or other law shall be controlling, but if no special election is so provided for the filling of vacancies, this section shall control.