Offer including new tie (4)
I believe the answer is:
bind
'tie' is the definition.
('bind' can be a synonym of 'tie')
'offer including new' is the wordplay.
'offer' becomes 'bid' ('bid' can be a synonym of 'offer').
'including' indicates putting letters inside.
'new' becomes 'n'.
'bid' enclosing 'n' is 'BIND'.
(Other definitions for bind that I've seen before include "Fix" , "Tie, fasten" , "difficult situation" , "Join or fasten together" , "Tie together" .)