Repair damaged plaster behind door trim
You do not need to do anything to the plaster behind the trim. If you add anything to repair it, it will add thickness to the wall in that area and the trim will not fit as well. Once it is covered, you will not see it.... just as good as gone.

The thing will be is, be certain to nail the trim to the jamb with 4D nails and 8 or10D nails through the plaster. Do not nail where the plaster is missing, it will be prone to cracking the trim, the wall must be solid where you nail. Pilot holes will be handy, but can be done without.