Crazy person going back to New York for fish (5)
I believe the answer is:
tunny
'for fish' is the definition.
(tunny is a kind of fish)
'crazy person going back to new york' is the wordplay.
'crazy person' becomes 'nut' (nut can informally mean an insane person).
'going back' is a reversal indicator.
'to new york' becomes 'ny'.
'nut' back-to-front is 'tun'.
'tun'+'ny'='TUNNY'
(Other definitions for tunny that I've seen before include "Large marine fish" , "A tuna" , "Warm water food fish" , "Common food fish" , "Marine fish, the bluefin" .)