The most common and most likely answer to this crossword clue is the 11 letter word ANAESTHESIA
I've seen this crossword clue in The Times
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More clues leading to the result ANAESTHESIA
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The straight part
We know that "Effect of drugs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case effect of drugs = anaesthesia.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 ANAESTHESIA mean?
ANAESTHESIA noun- An artificial method of preventing sensation, used to eliminate pain without causing loss of vital functions, by the administration of one or more agents which block pain impulses before transmitted to the brain.
- The loss or prevention of sensation, as caused by anesthesia, lesion in the nervous system or other physical abnormality.