Ignores rent for cheap shop (8,5)
I believe the answer is:
discount store
'cheap shop' is the definition.
(shop where things are sold at discount prices)
'ignores rent' is the wordplay.
'ignores' becomes 'discounts' ('discount' can be a synonym of 'ignore').
'rent' becomes 'tore' ('rend' and 'tear' both mean to rip something).
'discounts'+'tore'='DISCOUNT STORE'
'for' is the link.
(Other definitions for discount store that I've seen before include "Shop offering goods at reduced prices" , "place with low prices" , "retail outlet" .)