I have this cracked corner. To the left is door molding. To the right is a built-in closet. I believe the wall is plaster.
How do I fix this corner?
Caulk.
But before you do that, ask yourself what the reason for the crack may be, and if it's a symptom of something more sinister. Dry rot? Termites? Foundation shifting? Someone with anger management problems slamming the closet doors?
Of course it may be nothing, in which case you can either patch the entire wall from trim to trim, or just dig out the crack, remove as much dust as possible, paint with white glue to seal the surface and put in several layers of common painter's caulk over several days. I don't recommend plaster patch in this case, because this seam is likely to move again. You want something with some flex.
If the plaster is starting to separate from the walls, then Bill Wally has your answer over at : https://www.plastermagic.com/FAQs.html
If the crack opens up again, use a more flexible caulk (not just painter's caulk).
In construction generally, where two dissimilar materials meet, there will be movement.
The standard approach to handle the edge of plaster or drywall is to hace a molding cover the edge rather than butt up against it. Door casings serve that purpose in situations like yours. You have plaster butting up against the jamb with no overlapping casing.
I would solve this by placing a thin molding over the edge of the door jamb and to the left of the crack. Paint to match the existing door moldings.
If you do not want to do this, after scraping and evening the gap, it can be filled with caulk. But this is likely to look fairly makeshift and may open again.
