Plastering on existing painted walls is possible if the paint is in very good condition (in terms of adhesion).
Can You Plaster Over Painted Walls. The first thing you need to do is look at the condition of the wall your working on. As a decorator i have it done all the time.
How to Repair a Plaster Wall | how-tos | DIY from diy.sndimg.com
Let the filler/plaster dry hard, then sand the wall down, concentrating on a small area at a time. Then you can apply the venetian plaster or american clay or any other type plaster finish. Commonly used plaster applied over paint in the faux finish industry includes venetian plaster and drywall compound finishes.
This guide is about painting plaster walls.
So i am thinking of sanding tbh, it looks pretty rough, you can probably get it a bit better by filling and sanding, but its yep i've been there myself with pva splashed all over my newly plastered walls by the plasterer. The surface has a lot of uneven spots. Is there any grease or residue? Once dried we just painted over the plaster.