Tennessee Code Title 56. Insurance § 56-7-1204

(a) In the event of payment to any person under the coverage required by this part, and subject to the terms and conditions of the coverage, the insurer making payment shall, to the extent of the coverage, be subrogated to all of the rights of the person to whom payment has been made, and shall be entitled to the proceeds of any settlement or judgment resulting from the exercise of any rights of recovery of the person against any person or organization legally responsible for the bodily injury or property damage for which payment is made, including the proceeds recoverable from the assets of an insolvent insurer.

(b) Payment by an insurer under the coverage required by this part shall not constitute a satisfaction of the liability of the party or parties responsible for the bodily injury or property damage under the financial responsibility laws of this state.