Many liquids, when left undisturbed, form a skin on the surface. This is true with cans of paint, with meat broth, gravies, milk, custards… And that’s just a short list. Why a skin forms varies. With meat broth, for instance, the fat rises to the top and, as it cools, it congeals. The skin the forms on the surface of hot milk is especially disturbing to many.
This skin formation is due to the loss of solids that the milk undergoes as it is warmed up. As heat is applied to the milk, the proteins casein and beta-lactoglobulin start to coagulate, and form a skin on the surface. After further heating, the skin dries because of evaporation, and forms a still firmer barrier. ["Food for thought: Why does a skin form over hot milk?" in The Independent]
How to prevent skin from forming on the surface of liquid depends on the liquid. The web is full of tips for every liquid imaginable.
For custards, my solution is cling wrap.
I do this as soon as the custard is off the stove because the skin starts to form within minutes.
I take a sheet of cling wrap larger than the pan. I gently push the cling wrap so that every inch of the surface of the custard touches the plastic sheet. I cool the custard to room temperature then I chill it overnight in the fridge. No skin forms. At all.