Is an application required when there is an agreement to enter a protective order? This comes up when an agreed PO is part of a criminal plea agreement in a family violence case.

Why not make it a condition of the plea agreement if the agreement is for deferred or probation?

You can make the same prohibitions a condition of probation but you don't implicate some important protections that you have if you follow the family code.
The family code sets out the requirements for a protective order which starts with an application, service and notice of a hearing. The family code meets the federal requirements to be enforceable under federal law as well. The penal code refers back to a protective order issued pursuant to those provisions in the family code to be enforceable as a violation of a protective order 25.07 penal code.
The protective order under the family code also gives some protections for possession of a firearm even after being off probation and no longer subject to the protective order--see chapter 46 unlawful possession of a firearm

I would do both--make the provisions a violation of the probation and file your application and have a protective order granted for 2 years.