Attempt to keep new tie (4)
I believe the answer is:
bind
'tie' is the definition.
('bind' can be a synonym of 'tie')
'attempt to keep new' is the wordplay.
'attempt to' becomes 'bid'.
'keep' indicates putting letters inside.
'new' becomes 'n'.
'bid' going around 'n' is 'BIND'.
(Other definitions for bind that I've seen before include "Wrap tightly - nuisance" , "difficult situation" , "Fix" , "Tie up; annoyance" , "Tie, fasten" .)