Cryptic crossword clue
Each monk is embarrassed to have a dirty habit 5-5

The most common and most likely answer to this crossword clue is the 11 letter word CHAIN-SMOKE

I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "dirty habit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dirty habit = chain-smoke.
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 CHAIN-SMOKE mean?

CHAIN-SMOKE verb
  1. To smoke cigarettes by continuously lighting one from the glowing end of the previous one.
  2. To smoke tobacco cigarettes frequently.
  3. To smoke by continuously lighting one from another.

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