Title singer Jack rejected (7)
I believe the answer is:
baronet
'title' is the definition.
(I've seen this before)
'singer jack rejected' is the wordplay.
'singer' becomes 'tenor' (tenor is a kind of singer).
'jack' becomes 'ab' (both can mean a sailor).
'rejected' says the letters should be written backwards.
'tenor'+'ab'='tenorab'
'tenorab' reversed gives 'BARONET'.
(Other definitions for baronet that I've seen before include "Lower noble" , "Lowest hereditary title of honour" , "Lowest British hereditary title" , "Aristocrat" , "A Bronte (anag.)" .)