Stay with sweetheart following proposal (4)
I believe the answer is:
bide
'stay with' is the definition.
'sweetheart following proposal' is the wordplay.
'sweetheart' becomes 'e' (the middle letter or heart of 'sweet').
'following' says to put letters next to each other.
'proposal' becomes 'bid' (a bid is a proposal or offer).
'e' after 'bid' is 'BIDE'.
(Other definitions for bide that I've seen before include "To - one's time is to wait for the right opportunity" , "Dwell, of old" , "Remain or stay (poetically)" , "Stay (obs.)" , "Dwell, stay" .)