Tenn. Code Ann. § 8-48-102

On the death of any senator or representative from this state to the congress of the United States, or of any member of the general assembly, the county clerk of the county in which such officer, at the time of death, resided, shall give notice thereof to the governor; or on the death of the governor, such county clerk shall give notice to the speaker of the senate; and, in case of the death of any other officer, to the officer who is to fill the vacancy.