Dump detective overturning rival’s operations (7,2)
I believe the answer is:
dispose of
'dump' is the definition.
(thesaurus)
'detective overturning rival's operations' is the wordplay.
'detective' becomes 'di' (Detective Inspector abbreviation).
'overturning' says the letters should be written in reverse.
'rival's' becomes 'foes' (foe is a kind of rival).
'operations' becomes 'ops' (I have seen 'Military operations ' mean 'ops' so perhaps 'operations' could also mean 'ops').
'foes'+'ops'='foesops'
'foesops' reversed gives 'sposeof'.
'di'+'sposeof'='DISPOSE OF'
(Other definitions for dispose of that I've seen before include "Kill" , "Throw away" .)