Shop name in Italian city (4,2)
I believe the answer is:
turn in
'shop' is the definition.
(to shop someone is to turn them in to the police)
'name in italian city' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'in' is an insertion indicator.
'italian city' becomes 'turin' (I've seen this before).
'n' put into 'turin' is 'TURN-IN'.
(Other definitions for turn in that I've seen before include "Informally, go to bed or hand over" , "Surrender" , "Hit the hay" , "rat on" , "Go to bed, changing direction" .)