Food shop consignment with 50 per cent off (4)
I believe the answer is:
deli
'food shop' is the definition.
(short for delicatessen)
'consignment with 50 per cent off' is the wordplay.
'consignment' becomes 'delivery' (eg a consignment of goods).
'with 50 per cent off' indicates taking half.
'delivery' cut in half is 'DELI'.
(Other definitions for deli that I've seen before include "Cold-meat counter" , "Specialist food shop" , "Shop selling foreign foods" , "Food shop (colloq.)" , "Shop selling processed food products" .)