Offers to grab Romeo's tits, say (5)
I believe the answer is:
birds
'tits say' is the definition.
(tit is a kind of bird)
'offers to grab romeo's' is the wordplay.
'offers' becomes 'bids' (bid is a kind of offer).
'to grab' is an insertion indicator.
'romeo' becomes 'r' (phonetic alphabet: alpha, bravo, charlie etc.).
'bids' enclosing 'r' is 'BIRDS'.
(Other definitions for birds that I've seen before include "4th" , "eg Thrushes" , "Terns and tits, say" , "Gulls" , "... strictly receivers of rubbish" .)