The most common and most likely answer to this crossword clue is the 7 letter word BLITHER
I've seen this crossword clue in The Times
B
L
I
T
H
E
R
More clues leading to the result BLITHER
Buddy explains!

The straight part
We know that "Rabbit/more carefree" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rabbit/more carefree = blither.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 BLITHER mean?
BLITHER adjective- (dated or literary) Happy, cheerful.
- Casually indifferent, careless, showing a lack of concern.
- To talk foolishly; to blather