Irritate using a word of refusal in New York (5)
I believe the answer is:
annoy
'irritate' is the definition.
(synonyms)
'a word of refusal in new york' is the wordplay.
'word of refusal' becomes 'no'.
'in' is an insertion indicator.
'new york' becomes 'ny'.
'no' put within 'ny' is 'nnoy'.
'a'+'nnoy'='ANNOY'
'using' is the link.
(Other definitions for annoy that I've seen before include "Anger" , "Irritate - pester" , "Bug, rile" , "Upset" , "Irritate, needle" .)