Trainee state police officer cut short (5)
I believe the answer is:
cadet
'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').
'ca'+'det'='CADET'
(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" .)