The most common and most likely answer to this crossword clue is the 7 letter word MAUNDER
I've seen this crossword clue in The Guardian
M
A
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More clues leading to the result MAUNDER
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 = maunder.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 MAUNDER mean?
MAUNDER noun- A beggar.
- To speak in a disorganized or desultory manner; to babble or prattle.
- To wander or walk aimlessly.
- To beg; to whine like a beggar.