Hopeful lover, being rejected, goes off without you and I (6)
I believe the answer is:
suitor
'hopeful lover' is the definition.
'rejected goes off without you and i' is the wordplay.
'rejected' shows that the letters should be reversed in order.
'goes off' becomes 'rots'.
'without' indicates putting letters inside ('without' can be similar in meaning to 'outside').
'you' becomes 'u' (I've seen this in other clues**).
'and' is a charade indicator (letters next to each other) (I've seen this in other clues).
'u' after 'i' is 'iu'.
'rots' placed around 'iu' is 'rotius'.
'rotius' backwards is 'SUITOR'.
'being' is the link.
(Other definitions for suitor that I've seen before include ". . . he woos his girl" , "Man pursuing a woman for marriage" , "One seeking marriage" , "He pays court to a woman" , "Wooer" .)