The most common and most likely answer to this crossword clue is the 4 letter word DANK
D
A
N
K
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The straight part
We know that "Damp" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case damp = dank.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 DANK mean?
DANK noun- Moisture; humidity; water.
- Dark, damp and humid.
- (of marijuana) Highly potent.
- (often ironic) Great, awesome.
- To moisten, dampen; used of mist, dew etc.
- A small silver coin formerly used in Persia.