The most common and most likely answer to this crossword clue is the 3 letter word NIP
I've seen this crossword clue in The Times
N
I
P
Buddy explains!

The straight part
We know that "Small drink" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case small drink = nip.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 NIP mean?
NIP noun- A small quantity of something edible or a potable liquor.
- A nipple, usually of a woman.
- A playful bite.
- A pinch with the nails or teeth.
- Briskly cold weather.
- A seizing or closing in upon; a pinching
- A small cut, or a cutting off the end.
- A more or less gradual thinning out of a stratum.
- A blast; a killing of the ends of plants by frost.
- A biting sarcasm; a taunt.
- A short turn in a rope.
- (papermaking) The place of intersection where one roll touches another
- A pickpocket.
- To catch and enclose or compress tightly between two surfaces, or points which are brought together or closed; to pinch; to close in upon.
- To remove by pinching, biting, or cutting with two meeting edges of anything; to clip.
- To blast, as by frost; to check the growth or vigor of; to destroy.
- To annoy, as by nipping.
- To taunt.
- To squeeze or pinch.
- To steal; especially to cut a purse.
- To make a quick, short journey or errand, usually a round trip.