Tenn. Code Ann. § 67-8-209

If the Tennessee estate tax or any part thereof is paid, or collected out of that part of the Tennessee estate passing to or in possession of any person other than the executor or administrator in the executor's or administrator's capacity as such, such person shall be entitled to reimbursement out of any part of the Tennessee estate, still undistributed or paid, a just and equitable contribution by the persons whose interest in the estate of the decedent would have been reduced, if the tax had been paid before the distribution of the Tennessee estate, or whose interest is subject to equal or prior liability for the payment of taxes, debts, or other charges against the Tennessee estate.