Ace detectives may be bitter (4)
I believe the answer is:
acid
'be bitter' is the definition.
(acid can mean bitter-tasting)
'ace detectives' is the wordplay.
'ace' becomes 'a' (abbreviation).
'detectives' becomes 'CID' (abbreviation for Criminal Investigation Department).
'a'+'cid'='ACID'
'may' is the link.
(Other definitions for acid that I've seen before include "Sour - vitriolic" , "Polluted precipitation" , "Caustic and biting" , "So-called drug" , "bad rain" .)