Bit of fun with a bird (4)
I believe the answer is:
lark
This clue is a double definition.
'bit of fun' is the first definition.
(I've seen this before)
'a bird' is the second definition.
(lark is a kind of bird)
'with' acts as a link.
(Other definitions for lark that I've seen before include "Amusing adventure; bird" , "One singing high" , "Fool" , "Small songbird or playful action" , "Early riser" .)