Tenn. Code Ann. § 29-5-204

If the arbitration agreement provides a method of appointment of arbitrators, this method shall be followed. In the absence thereof, or if the agreed method fails or for any reason cannot be followed, or when an arbitrator appointed fails or is unable to act and the arbitrator's successor has not been duly appointed, the court on application of a party shall appoint one (1) or more arbitrators. An arbitrator so appointed has all the powers of one specially named in the agreement.