Shop fronts on dreary estate look inadequate (4)
I believe the answer is:
deli
'shop' is the definition.
(I know that deli is a type of shop)
'fronts on dreary estate look inadequate' is the wordplay.
'fronts on' says to take the initial letters (letters at the front).
The initial letters of 'dreary estate look inadequate' is 'DELI'.
(Other definitions for deli that I've seen before include "place to buy food" , "Specialised food shop" , "Fine-food store" , "Food shop (abbr)" , "Specialist foodshop(abbr.)" .)