Tex. Code of Criminal Procedure § 43.22

If the condemned person escapes after his delivery to the Director of the Department of Corrections, and is not retaken before the time appointed for his execution, any person may arrest and commit him to the Director of the Department of Corrections whereupon the Director of the Department of Corrections shall certify the fact of his escape and recapture to the court in which sentence was passed; and the court, either in term-time or vacation, shall again appoint a time for the execution which shall not be less than thirty days from the date of such appointment; and thereupon the clerk of such court shall certify such appointment to the Director of the Department of Corrections, who shall proceed at the time so appointed to execute the condemned, as hereinabove provided. The sheriff or other officer or other person performing any service under this and the preceding Article shall receive the same compensation as is provided for similar services under the provisions of Articles 1029 or 1030 of the Code of Criminal Procedure of 1925, as amended. If for any reason execution is delayed beyond the date set, then the court which originally sentenced the defendant may set a later date for execution.