Drug produced by a police department (4)
I believe the answer is:
acid
'drug' is the definition.
(acid is a kind of drug)
'by a police department' is the wordplay.
'by' says to put letters next to each other.
'police department' becomes 'CID' (abbreviation for Criminal Investigation Department).
'a' put next to 'cid' is 'ACID'.
'produced' is the link.
(Other definitions for acid that I've seen before include "Polluted precipitation" , "Bitter or sour" , "Caustic and biting" , "Vinegary" , "Tart, sour" .)