The most common and most likely answer to this crossword clue is the 8 letter word DIAZEPAM
D
I
A
Z
E
P
A
M
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The straight part
We know that "tranquillizer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tranquillizer = 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.