Detectives essentially split up (8)
I believe the answer is:
disperse
'split up' is the definition.
(thesaurus)
'detectives essentially' is the wordplay.
'detectives' becomes 'dis' (Detective Inspectors, DIs).
'essentially' becomes 'per se' (I've seen this in another clue).
'dis'+'perse'='DISPERSE'
(Other definitions for disperse that I've seen before include "Scatter or disband" , "Thin out and disappear" , "Scatter, disseminate" , "Broadcast" , "Scatter, dispel" .)