The most common and most likely answer to this crossword clue is the 10 letter word COTTONTAIL
I've seen this crossword clue in The Guardian
C
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Buddy explains!

The straight part
We know that "Rabbit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rabbit = cottontail.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 COTTONTAIL mean?
COTTONTAIL noun- A rabbit of any of various species in genus Sylvilagus.
- (nudism) A person with a tanned body and untanned buttocks, resembling a cottontail rabbit's dark fur and light tail.