The most common and most likely answer to this crossword clue is the 6 letter word BABBLE
B
A
B
B
L
E
Buddy explains!

The straight part
We know that "Rabbit on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rabbit on = babble.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 BABBLE mean?
BABBLE noun- Idle talk; senseless prattle
- Inarticulate speech; constant or confused murmur.
- A sound like that of water gently flowing around obstructions.
- To utter words indistinctly or unintelligibly; to utter inarticulate sounds
- To talk incoherently; to utter meaningless words.
- To talk too much; to chatter; to prattle.
- To make a continuous murmuring noise, like shallow water running over stones.
- To utter in an indistinct or incoherent way; to repeat words or sounds in a childish way without understanding.
- To reveal; to give away (a secret).