Last American in the Big Apple's a dope (5)
I believe the answer is:
ninny
'a dope' is the definition.
(I've seen this before)
'last american in the big apple's' is the wordplay.
'last' says to take the final letters.
'the big apple' becomes 'ny' (short for New York).
The last letter of 'american' is 'n'.
'n'+'in'+'ny'='NINNY'
(Other definitions for ninny that I've seen before include "Simpleton" , "dope" , "Silly billy" , "gravely so miscalled by mechanicals" , "not a wise man" .)