Man heading for the Big Apple (4)
I believe the answer is:
tony
'man' is the definition.
(man's name)
'heading for the big apple' is the wordplay.
'heading for' becomes 'to' (to head for a place is to go to it).
'the big apple' becomes 'ny' (short for New York).
'to'+'ny'='TONY'
(Other definitions for tony that I've seen before include "Shortened man's name" , "- - Adams, 7 legend" , "Classy" , "Blair; having style (slang)" , "Prime Minister of the UK" .)