Patience, mate. The single biggest cause of peeling, flaking paint on new plaster is painting too soon. Fresh plaster needs to be completely dry — and that means right through, not just on the surface.
As a rule, allow 4 to 6 weeks for new plaster to dry out. In a warm, well-ventilated room it can be quicker; in a cold, damp space — or a chunky skim over old walls — it'll take longer. The plaster goes from dark, patchy brown to a uniform pale pink as it cures. Don't even think about opening a tin until it's an even pale colour all over, with no dark damp patches lingering in corners or behind radiators. Crack the windows, keep some gentle heat on, and let it breathe. Don't blast it with a heat gun or whack the heating to max — drying it too fast causes cracking.
Once it's dry, you must seal it first. Fresh plaster is porous and sucks moisture out of paint like a sponge, which is what causes flaking. Skip the trade "drywall sealer" myths — the proper method is a mist coat: a quality matt emulsion thinned roughly 70:30 with water (70 paint, 30 water). Brands like Dulux and Crown matt emulsions mist down beautifully. If you're going breathable — and on lime or older walls you should — Earthborn Claypaint is brilliant straight over dry plaster and needs no separate sealer, just a thinned first coat.
The "but what about" question: skim coat over old painted walls dries faster, but the same dryness rule applies. And if you're chasing a flawless finish, your topcoat colour goes on after the mist coat has dried fully — two coats of something like Farrow & Ball Pointing or Little Greene Slaked Lime will sit perfectly once the wall's properly prepped.
Rush it and you'll be stripping it back in six months. Wait it out and seal it right — sorted.