The most common and most likely answer to this crossword clue is the 6 plus 6 letter word PUBLIC SCHOOL
I've seen this crossword clue in The Guardian
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Buddy explains!
The straight part
We know that "Privileged place" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case privileged place = public school.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 PUBLIC SCHOOL mean?
PUBLIC SCHOOL noun- Certain private schools, particularly (initially) any grammar school operated apart from the personal lands of its students or (from the 19th century) the feepaying secondary schools which developed from or were modelled upon them; a British boarding school
- A college or university
- (formerly Scottish) A publicly funded and administered school; such schools in the context of other countries