Tex. Estates Code § 361.102

(a) If a person appointed as personal representative fails to qualify or, after qualifying, dies, resigns, or is removed, the court may, on application, appoint a successor representative if the appointment of a successor is necessary. The appointment may be made before a final accounting is filed or before any action on a final accounting is taken. In the event of death, the legal representatives of the deceased personal representative shall account for, pay, and deliver all estate property that was entrusted to the deceased personal representative's care to the persons legally entitled to receive the property, at the time and in the manner ordered by the court.

(b) The court may appoint a successor representative under this section without citation or notice if the court finds that the immediate appointment of a successor representative is necessary.