Vote of American in New York (3)
I believe the answer is:
nay
'vote' is the definition.
(I've seen this in another clue)
'american in new york' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'in' means one lot of letters goes inside another.
'new york' becomes 'ny'.
'a' going within 'ny' is 'NAY'.
'of' acts as a link.
(Other definitions for nay that I've seen before include "Negative answer" , "Indeed" , "disagreement" , "No - a negative vote" , "In point of fact - a parliamentary vote against" .)