The most common and most likely answer to this crossword clue is the 3 letter word DEW
I've seen this crossword clue in The Daily Telegraph
D
E
W
Buddy explains!
The straight part
We know that "dampness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dampness = dew.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 DEW mean?
DEW noun- Any moisture from the atmosphere condensed by cool bodies upon their surfaces.
- Moisture in the air that settles on plants, etc in the morning, resulting in drops.
- (but see usage notes) An instance of such moisture settling on plants, etc.
- Anything that falls lightly and in a refreshing manner.
- An emblem of morning, or fresh vigour.
- To wet with, or as if with, dew; to moisten.