The most common and most likely answer to this crossword clue is the 7 letter word SHOWERY
I've seen this crossword clue in The Guardian
S
H
O
W
E
R
Y
More clues leading to the result SHOWERY
Buddy explains!

The straight part
We know that "wet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wet = showery.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 SHOWERY mean?
SHOWERY adjective- Given to showers; having frequent rainfall.
- Of or relating to a shower or showers.