Artilleryman losing head in New York convent (7)
I believe the answer is:
nunnery
'convent' is the definition.
(nunnery is a kind of convent)
'artilleryman losing head in new york' is the wordplay.
'artilleryman' becomes 'gunner' ('gunner' can be a synonym of 'artilleryman').
'losing head' means to remove the first letter.
'in' is an insertion indicator.
'new york' becomes 'ny'.
'gunner' with its initial letter removed is 'unner'.
'unner' inserted into 'ny' is 'NUNNERY'.
(Other definitions for nunnery that I've seen before include "Convent" , "Hamlet to Ophelia: 'Get thee to a . . . . . . .'" , "Female religious house" , "sisters' place" , "Religious house for females" .)