Police ran Vice with a difference (8)
I believe the answer is:
variance
'difference' is the definition.
(variance is a kind of difference)
'police ran vice with a' is the wordplay.
'police' indicates an anagram (police can mean to control or manage).
'with' is an insertion indicator.
'ran'+'vice'='ranvice'
'ranvice' with letters rearranged gives 'varince'.
'varince' enclosing 'a' is 'VARIANCE'.
(Other definitions for variance that I've seen before include "Not the main attraction" , "Discrepancy, divergence" , "Dissension" , "Difference, discrepancy" , "Change" .)