Texas Estates Code - EST § 51.051. Personal Service

(a) Except as otherwise provided by Subsection (b), if personal service of citation or notice is required, the citation or notice must be served on the attorney of record for the person to be cited or notified.  Notwithstanding the requirement of personal service, service may be made on that attorney by any method specified by Section 51.055 for service on an attorney of record.

(b) If the person to be cited or notified does not have an attorney of record in the proceeding, or if an attempt to serve the person's attorney is unsuccessful:

(c) The return day of the citation or notice served under Subsection (b) must be at least 10 days after the date of service, excluding the date of service.

(d) If citation or notice attempted to be served as provided by Subsection (b) is returned with the notation that the person sought to be served, whether inside or outside this state, cannot be found, the county clerk shall issue a new citation or notice.  Service of the new citation or notice must be made by publication.