Sweetheart, first to be dumped and done with (4)
I believe the answer is:
over
'done with' is the definition.
(similar in meaning as in 'over and done with')
'sweetheart first to be dumped' is the wordplay.
'sweetheart' becomes 'lover' (sweetheart can mean a lover).
'first to be dumped' means to remove the first letter.
'lover' with its initial letter taken away is 'OVER'.
'and' is the link.
(Other definitions for over that I've seen before include "Period of play" , "left for another day?" , "Half a dozen deliveries" , "bowling unit" , "See 12" .)