The most common and most likely answer to this crossword clue is the 4 letter word GLUG
G
L
U
G
Buddy explains!

The straight part
We know that "Drink" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case drink = glug.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 GLUG mean?
GLUG noun- The sound made when a significant amount of liquid is poured suddenly out of something, such as a jug or bottle.
- The amount of liquid issued when the "glug" sound is heard.
- To flow in noisy bursts.
- To quickly swallow liquid.