Asked to offer a room (6)
I believe the answer is:
bidden
'asked' is the definition.
(I've seen this before)
'offer a room' is the wordplay.
'offer' becomes 'bid' (bid is a kind of offer).
'a room' becomes 'den' (den is a kind of room).
'bid'+'den'='BIDDEN'
'to' is the link.
(Other definitions for bidden that I've seen before include "Ordered (to)" , "Asked" , "Commanded (to do something)" .)