Trainee detective comes up without notice (5)
I believe the answer is:
Here is my best explanation:
'trainee' is the definition.
(cadet is a kind of trainee)
'detective comes up without notice' is the subsidiary indication.
'detective' becomes 'tec' ('tec' can be a synonym of 'detective').
'comes up' is a reversal indicator.
'without' means one lot of letters goes inside another.
'notice' becomes 'ad'.
'tec' written backwards gives 'cet'.
'cet' placed around 'ad' is 'cadet'.
(Other definitions for cadet that I've seen before include "Trainee officer", "Younger brother", "Officer-trainee", "Military trainee officer", "Trainee cop", "Younger son's branch of a family", "Trainee -- acted (anag)", "Army trainee", "Young trainee, eg in the police" and "A trainee army officer".)