The most common and most likely answer to this crossword clue is the 9 letter word NIGHTCAPS
I've seen this crossword clue in The Times
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More clues leading to the result NIGHTCAPS
Buddy explains!

The straight part
We know that "Drinks late on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case drinks late on = nightcaps.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does NIGHTCAPS mean?
NIGHTCAPS noun- A warm cloth cap worn while sleeping, often with pajamas, being common attire in northern Europe before effective home heating became widespread.
- A beverage drunk before bed that is usually alcoholic.
- (by extension) Something the person reads or listens to before bed.
- The final match of a sporting contest, especially the second game of a baseball doubleheader.
- A cap drawn over the face of the condemned person before they are hanged.