A thorough job would involve scrapping, then prime, finally finishing it with paint.

Typically contractors would save cost with maxilite as a primer but if it's for your own stay and you want it to last and have a good finish then I suppose a good primer is just as important.

A simple quick job would be to just scape away the peeling part then paint it over with existing paint to cover up

That fine wood grain...very likely of termite infestation