Drug cops did lates with absolutely no cover (6)

I believe the answer is:

opiate

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'drug' is the definition.
(opiate is a kind of drug)

I can't explain the rest of the clue.

(Other definitions for opiate that I've seen before include "A drug to induce sleep" , "Narcotic, such as morphine" , "Drug made from poppy" , "Poppy-based drug" , "Preparation made from poppy derivative" .)

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