Tennessee law requires that sales or use tax be paid on aircraft domiciled in Tennessee. If your purchase was from an aircraft dealer in Tennessee, tax was probably collected by the dealer. If your purchase was from an individual who is not a dealer or from an out-of-state dealer or individual, you are required to pay tax directly to the Department of Revenue.
Tennessee residents are required to file an Affidavit of Transfer on all purchases and sales of aircraft even if the transactions are exempt. The seller signature is not required on the Affidavit filed by the purchaser. The Affidavit or Transfer of Aircraft can be found here.