The most common and most likely answer to this crossword clue is the 9 letter word ABSTAINER
I've seen this crossword clue in The Daily Telegraph
A
B
S
T
A
I
N
E
R
More clues leading to the result ABSTAINER
- One staying dry in rain: beats getting buffeted!
- One practising self-denial in a British town? Almost right
- Spot, in Aberdeen, half-cut, one usually of temperate habits?
- Seat in bar maybe not his?
- Party-pooper, in more ways than one!
- Jack, one making a mark, one that doesn’t count in 8
- Rechabite cooked bairn’s tea
- Band of Hope member ordered teas in bar
- Spilled Brian’s tea — he won’t have a drink
- Person who won’t indulge reserved seat in bar
Buddy explains!

The straight part
We know that "he won’t have a drink" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case he won’t have a drink = abstainer.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.