Cryptic crossword clue
Exclusive group of people governing stylish private hospital 8

The most common and most likely answer to this crossword clue is the 8 letter word CLINIQUE

I've seen this crossword clue in Financial Times
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Buddy explains!

The straight part
We know that "private hospital" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case private hospital = clinique.
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.

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