The most common and most likely answer to this crossword clue is the 8 letter word KETAMINE
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The straight part
We know that "anaesthetic" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case anaesthetic = ketamine.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 KETAMINE mean?
KETAMINE noun- A pain-killing drug and anaesthetic, (RS)-2-(2-chlorophenyl)-2-(methylamino)cyclohexanone, commonly used recreationally.