The most common and most likely answer to this crossword clue is the 6 letter word SLEWED
S
L
E
W
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D
More clues leading to the result SLEWED
Buddy explains!

The straight part
We know that "drunk" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case drunk = slewed.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 SLEWED mean?
SLEWED verb- To rotate or turn something about its axis.
- To veer a vehicle.
- To insert extra ticks or skip some ticks of a clock to slowly correct its time.
- To pivot.
- To skid.
- To move something (usually a railway line) sideways
- To make a public mockery of someone through insult or wit.
- Somewhat drunk; tipsy.