Tenant without cover for expense (6)
I believe the answer is:
lessee
'tenant' is the definition.
(I know that lessee is a type of tenant)
'without cover for expense' is the wordplay.
'without' becomes 'less' (I've seen this in another clue).
'cover for' suggests removing the centre.
'expense' with its centre taken out is 'ee'.
'less'+'ee'='LESSEE'
(Other definitions for lessee that I've seen before include "One granted temporary use of property" , "Tenant who holds a lease" , "One holds a lease" , "Who pays the rent" , "Hirer of property" .)