Irritate a small number in US city (5)
I believe the answer is:
annoy
'irritate' is the definition.
(I know that irritate can be written as annoy)
'a small number in us city' is the wordplay.
'small number' becomes 'no' (abbreviation for 'number').
'in' indicates putting letters inside.
'us city' becomes 'ny' (short for New York).
'no' placed within 'ny' is 'nnoy'.
'a'+'nnoy'='ANNOY'
(Other definitions for annoy that I've seen before include "Gall" , "Anger" , "Nark - nettle" , "Vex" , "Irk" .)