Offer to acquire new tie (4)
I believe the answer is:
bind
'tie' is the definition.
(synonyms)
'offer to acquire new' is the wordplay.
'offer' becomes 'bid' (synonyms).
'to acquire' is an insertion indicator.
'new' becomes 'n'.
'bid' going around 'n' is 'BIND'.
(Other definitions for bind that I've seen before include "difficult situation" , "difficulty" , "Senior figure" , "Tie together" , "Tie up; annoyance" .)