Detectives to fix deterioration (9)
I believe the answer is:
disrepair
'deterioration' is the definition.
(thesaurus)
'detectives to fix' is the wordplay.
'detectives' becomes 'dis' (Detective Inspectors, DIs).
'to fix' becomes 'repair' (to fix something is to repair it).
'dis'+'repair'='DISREPAIR'
(Other definitions for disrepair that I've seen before include "State of collapse" , "In need of mending" , "Degradation" , "poor state" , "state of neglect" .)