Trainee state police officer cut short (5)
I believe the answer is:
'trainee' is the definition.
(cadet is a kind of trainee)
'state police officer cut short' is the wordplay.
'state' becomes 'ca' (abbreviation for California).
'police officer cut short' becomes 'det' (shortened form of 'detective').
(Other definitions for cadet that I've seen before include "Junior officer; younger brother" , "aspiring officer" , "Young trainee, eg in the police" , "Younger son's branch of a family" , "Apprentice officer" .)