What is other words for under aged drinking?

Answer 1

Under-age drinking doesn't have a synonym: together they form one noun: "under-age drinking" which is difficult to describe in another way.

You could, however, talk about minors drinking illegally, and potentially use words like "adolescents", "under 16/18/21's", "children" or "young people". However, these nouns are vague, and don't refer specifically to the law itself.

People know what "under-age drinking" means, so it may be best to keep using this same phrase to make sure you don't lose your reader/listener in a web of synonyms.