Offers to cage rook or rooks? (5)
I believe the answer is:
birds
'rooks?' is the definition.
(rook is a kind of bird)
'offers to cage rook' is the wordplay.
'offers' becomes 'bids' ('bid' can be a synonym of 'offer').
'to cage' means one lot of letters goes inside another (inserted letters are locked up).
'rook' becomes 'r' (abbreviation in chess).
'bids' placed around 'r' is 'BIRDS'.
'or' is the link.
(Other definitions for birds that I've seen before include "Things may be strictly for them!" , "eg Thrushes" , "Terns and tits, say" , "... strictly receivers of rubbish" , "Egg-laying vertebrates" .)