Detective inspectors try to show revulsion (8)
I believe the answer is:
'revulsion' is the definition.
(distaste can mean a feeling of revulsion)
'detective inspectors try' is the wordplay.
'detective inspectors' becomes 'DIs' (abbreviation).
'try' becomes 'taste' (synonyms).
'to show' acts as a link.
(Other definitions for distaste that I've seen before include "Abhorrence" , "Mild horror" , "Antipathy, aversion" , "Feeling of dislike - unsavoury?" , "Is stated (anag.)" .)