Offer to wrap new tie (4)
I believe the answer is:
bind
'tie' is the definition.
('bind' can be a synonym of 'tie')
'offer to wrap new' is the wordplay.
'offer' becomes 'bid' ('bid' can be a synonym of 'offer').
'to wrap' means one lot of letters goes inside another.
'new' becomes 'n'.
'bid' enclosing 'n' is 'BIND'.
(Other definitions for bind that I've seen before include "Tie together" , "Tie; problem situation" , "Tie up; annoyance" , "Fix" , "This weed" .)