Tory with nothing on beginning to bother rabbit (6)
I believe the answer is:
confab
'rabbit' is the definition.
(both can mean to chat)
'tory with nothing on beginning to bother' is the wordplay.
'tory' becomes 'con' (abbreviation for conservative).
'with' means one lot of letters go next to another.
'nothing' becomes 'fa' (slang term - sweet Fanny Adams).
'on' says to put letters next to each other.
'beginning to' indicates taking the first letters.
The initial letter of 'bother' is 'b'.
'con'+'fa'+'b'='CONFAB'
(Other definitions for confab that I've seen before include "Informal discussion (colloq.)" , "casual conversation" , "Chatter" , "Chat (informal)" , "natter" .)