Shop beginning to suffer with rent (5)
I believe the answer is:
store
'shop' is the definition.
('store' can be a synonym of 'shop')
'beginning to suffer with rent' is the wordplay.
'beginning to' suggests taking the first letters.
'with' means one lot of letters go next to another.
'rent' becomes 'tore' ('rend' and 'tear' both mean to rip something).
The first letter of 'suffer' is 's'.
's'+'tore'='STORE'
(Other definitions for store that I've seen before include "Eg, granite" , "Stock or supply, or warehouse for them" , "Large shop; keep" , "Supermarket" , "Save" .)