Once you've left Hogwarts (or a foreign equivalent) you're about as good as magic as you're going to be. Hogwarts trains people to be wizards and witches, and once they've finished, that's normally how good you are. So there isn't really a regular system for improving adult characters - their magical education is over.
Having said that, some wizards can gain postgraduate magical training, for example, as an auror, or a healer. An established adult character can
apply for exceptional levels, if they can give a sufficient justification for having them. Alternatively, a character that has just left school can gain additional magical levels by regularly posting in a suitable forum (say, the Ministry, or St Mungo's) over a number of in-game years.
