Food shop on purpose having no carpet (4)
I believe the answer is:
deli
'food shop' is the definition.
(short for delicatessen)
'on purpose having no carpet' is the wordplay.
'on purpose' becomes 'deliberate' (I've seen this before).
'having no' indicates named letters should be taken away.
'carpet' becomes 'berate' (I've seen this before).
'deliberate' with 'berate' taken away is 'DELI'.
(Other definitions for deli that I've seen before include "Food store" , "Shop selling processed food products" , "place to buy food" , "Specialist foodshop(abbr.)" , "Food shop (abbr)" .)