Over-age means too old for a particular group, team, price or rule. A footballer can be over-age for the under-18 side; a traveller can be over-age for a child ticket; a class can close its door to anyone over-age. It is not a rude way to say “old.” You would not call a grandparent over-age at the dinner table. The word lives where there is a cut-off age written down. You will also see overage as one word. Its usual partner is underage — too young for the same kind of rule.