Tenn. Code Ann. § 71-5-2205

The county legislative body may remove the commissioners, or any one (1) of them, at pleasure, and proceed to fill the vacancy at any time; and should any one (1) or more of them die, resign, remove from the county, or fail or refuse to act, the county mayor may fill the vacancy, and such appointee shall continue to act as commissioner until an election by the legislative body.