The most common and most likely answer to this crossword clue is the 7 letter word LEGLESS
I've seen this crossword clue in The Times
L
E
G
L
E
S
S
More clues leading to the result LEGLESS
Buddy explains!

The straight part
We know that "Very drunk" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very drunk = legless.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 LEGLESS mean?
LEGLESS adjective- Without legs.
- Too drunk to stand.