The most common and most likely answer to this crossword clue is the 8 letter word DIAZEPAM
I've seen this crossword clue in Financial Times
D
I
A
Z
E
P
A
M
Buddy explains!

The straight part
We know that "drug" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case drug = diazepam.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does DIAZEPAM mean?
DIAZEPAM noun- A tranquilizing muscle relaxant drug (trademark Valium) used chiefly to relieve anxiety.