The most common and most likely answer to this crossword clue is the 11 letter word STAR-STRUCK
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More clues leading to the result STAR-STRUCK
Buddy explains!

The straight part
We know that "captivated by famous people" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case captivated by famous people = star-struck.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 STAR-STRUCK mean?
STAR-STRUCK adjective- Under the malevolent influence of the stars or of one's horoscope
- Fascinated and/or obsessed by fame or by celebrities; awed by an encounter with a celebrity