The most common and most likely answer to this crossword clue is the 5 letter word ARHAT
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More clues leading to the result ARHAT
Buddy explains!

The straight part
We know that "enlightened monk" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case enlightened monk = arhat.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 ARHAT mean?
ARHAT noun- One who has attained enlightenment; a Buddhist saint.
- One of the stages of the ascetic's spiritual evolution, when all passions (anger, ego, deception, greed, attachment, hatred and ignorance) are destroyed; arhanta.