The most common and most likely answer to this crossword clue is the 13 letter word STERILISATION
I've seen this crossword clue in Financial Times
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Buddy explains!
The straight part
We know that "Cleansing procedure" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cleansing procedure = sterilisation.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 STERILISATION mean?
STERILISATION noun- The process of treating something to kill or inactivate microorganisms.
- A procedure to permanently prevent an organism from reproducing.
- An instance of a sterilization procedure
- A monetary policy operation used to offset a foreign exchange intervention.