Racket discovered by a police inspector at the detention centre (3)
I believe the answer is:
din
'racket' is the definition.
(both can mean a loud noise or disturbance)
'inspector at the detention centre' is the wordplay.
'inspector' becomes 'di' (abbreviation for Detective Inspector).
'at' is a charade indicator (letters next to each other).
'centre' indicates the central letters.
The centre of 'detention' is 'n'.
'di'+'n'='DIN'
'discovered by a police' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for din that I've seen before include "speed in film" , "Unwanted noise" , "Loud noise, racket" , "Roar of confused noises" , "Loud and long noise" .)