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 wordplay.
'detective' becomes 'tec' ('tec' can be a synonym of 'detective'**).
'comes up' shows that the letters should be reversed in order.
'without' means one lot of letters goes inside another ('without' can be similar in meaning to 'outside').
'notice' becomes 'ad'.
'tec' reversed gives 'cet'.
'cet' placed around 'ad' is 'CADET'.
(Other definitions for cadet that I've seen before include "Trainee soldier", "who needs to be properly trained?", "Trainee officer", "Army trainee", "A trainee army officer", "Trainee -- acted (anag)", "recruit", "not the heir", "Military trainee officer" and "Officer-trainee".)