The most common and most likely answer to this crossword clue is the 8 letter word CONCLAVE
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The straight part
We know that "Secret meeting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case secret meeting = conclave.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 CONCLAVE mean?
CONCLAVE noun- The set of apartments within which the cardinals of the Roman Catholic Church are continuously secluded while engaged in choosing a pope.
- The group of Roman Catholic cardinals locked in a conclave until they elect a new pope; the body of cardinals.
- A private meeting; a close or secret assembly.