Distemper is an old form of paint (chalk based) and is generally found in older properties when several layers of wallpaper or woodchip are removed. It does not bond well directly to new plaster and should either be removed or sealed.
The most important part is the preparation prior to plastering because if the correct bonding agent is not used then the plaster skim could easily crack or blister and, in some cases, peel away from the wall altogether.
Our preference is to seal the distemper properly with an oil-based primer/sealer. Apply by brush/small roller (do not dilute) and once dry, we apply a strong sand based pre-plastering bonding agent which is ideal for this type of surface to give additional key/grip. This will require two decent coats and must be left to dry for at least 24 hours and plastering can only commence once this is completely dry.
It is a detailed and careful process but if the Distemper is not sealed properly then the plaster can simply blister causing paint to flake and, if wallpapering, fail to adhere properly.
Plastering Over Old Lead Paint
The same treatment as Plastering Over Distemper is used because if you try and bond with PVA, in our experience it is found that the PVA just hangs from the old lead paint surface and does not create a proper bond for plastering.