Detective must abandon vague feeling (8)
I believe the answer is:
instinct
'feeling' is the definition.
(an instinct is a feeling or sensation)
'detective must abandon vague' is the wordplay.
'detective' becomes 'di' (Detective Inspector abbreviation).
'must abandon' is a deletion indicator.
'vague' becomes 'indistinct'.
'indistinct' with 'di' taken away is 'INSTINCT'.
(Other definitions for instinct that I've seen before include "Flair" , "Nose" , "Gut feeling" , "Innate behavioural pattern" , "Innate reaction" .)