Man with a bill returned by the trainee
I believe the answer is:
cadet
'the trainee' is the definition.
(cadet is a kind of trainee)
'man with a bill returned' is the wordplay.
'man' becomes 'ted' (Ted is a man's name).
'with' says to put letters next to each other.
'a bill' becomes 'ac' (short for account).
'returned' shows that the letters should be reversed in order.
'ted'+'ac'='tedac'
'tedac' written backwards gives 'CADET'.
'by' is the link.
(Other definitions for cadet that I've seen before include "Officer-trainee" , "Younger son" , "Armed services trainee" , "Younger member of family" , "One in training" .)