The most common and most likely answer to this crossword clue is the 13 letter word ANTIHISTAMINE
I've seen this crossword clue in The Daily Telegraph
A
N
T
I
H
I
S
T
A
M
I
N
E
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 = antihistamine.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 ANTIHISTAMINE mean?
ANTIHISTAMINE noun- A drug or substance that counteracts the effects of a histamine. Commonly used to alleviate the symptoms of hay fever and other allergies.