Tenant perhaps offering regular payment to save face (8)
I believe the answer is:
resident
'tenant perhaps' is the definition.
(tenant is a kind of resident)
'regular payment to save face' is the wordplay.
'regular payment' becomes 'rent' (rent is a kind of regular payment).
'to save' means one lot of letters goes inside another.
'face' becomes 'side' ('side' can be a synonym of 'face'**).
'rent' going around 'side' is 'RESIDENT'.
'offering' is the link.
(Other definitions for resident that I've seen before include "Citizen" , "Local" , "Denizen" , "always in memory" , "Inmate" .)