Sweetheart ran, ran away (6)
I believe the answer is:
eloped
'ran away' is the definition.
(I've seen this in another clue)
'sweetheart ran' is the wordplay.
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'ran' becomes 'loped' (loping is a kind of running).
'e'+'loped'='ELOPED'
(Other definitions for eloped that I've seen before include "Ran away to get married" , "Went off" , "Ran away to marry" .)