New leader leaves artillery where order is put up (7)
I believe the answer is:
nunnery
'where order is put up' is the definition.
(residence for an order of nuns)
'new leader leaves artillery' is the wordplay.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'leader leaves' means to remove the first letter.
'artillery' becomes 'gunnery'.
'gunnery' with its first letter removed is 'unnery'.
'n'+'unnery'='NUNNERY'
(Other definitions for nunnery that I've seen before include "sisters' place" , "Hamlet to Ophelia: 'Get thee to a . . . . . . .'" , "Convent" , "Religious establishment" , "Religious house for females" .)