Food shop I managed in recession (4)
I believe the answer is:
deli
'food shop' is the definition.
(short for delicatessen)
'i managed in recession' is the wordplay.
'managed' becomes 'led' (lead can mean to manage or be in charge).
'in recession' says the letters should be written in reverse (letters recede or go back).
'i'+'led'='iled'
'iled' in reverse letter order is 'DELI'.
(Other definitions for deli that I've seen before include "Shop selling processed food products" , "Cold-meat counter" , "small food shop" , "part of supermarket" , "Specialised food shop" .)