Rejected sweetheart can start to get offensive (9)
I believe the answer is:
revolting
'offensive' is the definition.
('revolting' can be similar in meaning to 'offensive')
'rejected sweetheart can start to get' is the wordplay.
'rejected' says the letters should be written backwards.
'sweetheart' becomes 'lover' (I've seen this before**).
'can' becomes 'tin' ('tin' can be a synonym of 'can').
'start to' indicates taking the first letters.
The initial letter of 'get' is 'g'.
'lover' backwards is 'revol'.
'revol'+'tin'+'g'='REVOLTING'
(Other definitions for revolting that I've seen before include "Disgusting" , "Loathsome" , "Repulsive" , "rioting" , "Rising in rebellion" .)