Sharp as a police department (4)
I believe the answer is:
acid
'sharp' is the definition.
(as in sharp-tasting)
'a police department' is the wordplay.
'police department' becomes 'CID' (abbreviation for Criminal Investigation Department).
'a'+'cid'='ACID'
'as' acts as a link.
(Other definitions for acid that I've seen before include "Chemical compound" , "Bitter or sour" , "- - -drop, sweet" , "Cutting" , "Sour, sharp-tasting" .)