The most common and most likely answer to this crossword clue is the 10 letter word SKINNY-DIP
I've seen this crossword clue in The Times
S
K
I
N
N
Y
-
D
I
P
Buddy explains!

The straight part
We know that "Uncovered dive, possibly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case uncovered dive, possibly = skinny-dip.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 SKINNY-DIP mean?
SKINNY-DIP verb- To swim naked.