Big booby's little bird (5,3)
I believe the answer is:
great tit
'bird' is the definition.
(I've seen this before)
'big booby's little' is the wordplay.
'big' becomes 'great' (similar in meaning).
'booby's little' becomes 'tit' (I can't explain this - if you can you should believe this answer much more).
'great'+'tit'='GREAT TIT'
Can you help me to learn more?
(Other definitions for great tit that I've seen before include "Black-headed bird" , "A bird; target it (anag)" , "Common small bird with yellow breast" , "Bird changed" , "Small songbird" .)