Once a criminal record is expunged can I apply for a government job such as a police officer in TX?

Unless this was a theft case for less than $50 (a Class C Theft) then this is not a case that could have been expunged. To be eligible for an expunction the charge against a person must result in a dismissal (without any terms and conditions of probation being ordered under section 42.12), or an acquittal. There are other qualifying cases, but those are the most common. If you were on deferred, you are likely eligible only to have the records sealed via a Petition for Non-Disclosure. If it was a Class C Theft, and the charges against you were deferred after the probationary period, and the expunction process has run its course, then yes, you should be able to apply for a job as a police officer. If it was any other type of probation (Class B or up; discharged via a 42.12 probation) you can still apply. It is just likely they will be able to see the offense and disposition. In that case you will simply need to disclose the offense to the place where you intend to apply.