Unattached police on island (8)
I believe the answer is:
discrete
'unattached' is the definition.
(thesaurus)
'police on island' is the wordplay.
'police' becomes 'dis' (detective inspectors or DIs).
'on' is a charade indicator (letters next to each other).
'island' becomes 'crete' (Crete is an example**).
'dis'+'crete'='DISCRETE'
(Other definitions for discrete that I've seen before include "Secret ID (anag) - separate" , "Individually self-contained in discreet way" , "Unattached" , "Individually distinct in discreet way" , "Individually distinct, maybe discreet" .)