The most common and most likely answer to this crossword clue is the 3 letter word TOT
I've seen this crossword clue in The Times
T
O
T
Buddy explains!

The straight part
We know that "Little booze" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case little booze = tot.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 TOT mean?
TOT noun- A small child.
- A measure of spirits, especially rum.
- Tater tot.
- A foolish fellow.
- A total, an addition of a long column of figures.
- To sum or total.
- To mark (a debt) with the word tot (Latin for "so much"), indicating that it was good or collectible for the amount specified.