Detectives lost out (9)
I believe the answer is:
dismissed
'out' is the definition.
'detectives lost' is the wordplay.
'detectives' becomes 'dis' (Detective Inspectors, DIs).
'lost' becomes 'missed' ().
'dis'+'missed'='DISMISSED'
(Other definitions for dismissed that I've seen before include "Brushed off or sacked" , "Fired" , "Spurned" , "put out of court" .)