Hi @DIYBlake,
Welcome to the Bunnings Workshop community, it is fantastic to have you with us.
Typically, you would install an architrave around a door to conceal the cut ends of plasterboard, but your door frame appears to be designed with a shadow gap and no door jamb.
I'm a little bit confused by the gap around your door. Is it possible to get a photo from a bit further back showing the entire door?
Where a piece of plasterboard simply ends with a gap, the typical method would be to attach a Casing Bead to encapsulate the cut end. In your situation, you may have to back out the screws so you can slip a bead with some Corner Bead Spray Adhesive onto the end of the plasterboard and then screw it back in place.
You would then apply some no more gaps to seal up the seam on its top edge before painting.
This could be an option in your situation, but I would need to see the whole door to see if it would be the best option.
I will assist further when I can see the whole door.
Jacob
