Texas Property Code - PROP § 113.083. Appointment of Successor Trustee

(a) On the death, resignation, incapacity, or removal of a sole or surviving trustee, a successor trustee shall be selected according to the method, if any, prescribed in the trust instrument. If for any reason a successor is not selected under the terms of the trust instrument, a court may and on petition of any interested person shall appoint a successor in whom the trust shall vest.

(b) If a vacancy occurs in the number of trustees originally appointed under a valid charitable trust agreement and the trust agreement does not provide for filling the vacancy, the remaining trustees may fill the vacancy by majority vote.