Bird's after big time lush (7)
I believe the answer is:
ostrich
'bird's' is the definition.
(ostrich is a kind of bird)
'after big time lush' is the wordplay.
'after' means one lot of letters go next to another.
'big' becomes 'os'.
'time' becomes 't'.
'lush' becomes 'rich' ('rich' can be similar in meaning to 'lush').
'os'+'t' is 'ost'.
'ost'+'rich'='OSTRICH'
(Other definitions for ostrich that I've seen before include "Person refusing to face reality" , "The biggest bird, can't fly" , "Chorist (anag.)" , "Runner" , "Creature" .)