The most common and most likely answer to this crossword clue is the 12 letter word SOPHISTICATE
I've seen this crossword clue in The Times
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More clues leading to the result SOPHISTICATE
Buddy explains!

The straight part
We know that "one in fashionable set" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one in fashionable set = sophisticate.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 SOPHISTICATE mean?
SOPHISTICATE noun- A worldly-wise person.
- To make less natural or innocent.
- To practice sophistry; change the meaning of, or be vague about in order to mislead or deceive.
- To alter and make impure, as with the intention to deceive.
- To make more complex or refined.
- Adulterated; not pure; not genuine.