The most common and most likely answer to this crossword clue is the 6 letter word YABBER
I've seen this crossword clue in The Times
Y
A
B
B
E
R
More clues leading to the result YABBER
Buddy explains!

The straight part
We know that "to rabbit on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to rabbit on = yabber.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 YABBER mean?
YABBER verb- To talk, jabber.