Tennessee Code Title 6. Cities and Towns § 6-3-107

(b)(1) By affirmative vote of a majority of the remaining members, the board shall fill a vacancy in the office of alderman for the unexpired term, but any portion of an unexpired four-year term for alderman or mayor that remains beyond the next municipal election shall be filled by the voters at that election, if the vacancy occurs at least twenty (20) days before the latest time for filing nominating petitions for candidates in that election.

(2) All such elections by the board shall be made by voice vote, on the calling of the roll. If a tie vote occurs in filling a vacancy on the board, the presiding officer shall vote a second time to break the tie.