The most common and most likely answer to this crossword clue is the 11 letter word PERSONALITY
I've seen this crossword clue in The Daily Telegraph
P
E
R
S
O
N
A
L
I
T
Y
More clues leading to the result PERSONALITY
Buddy explains!
The straight part
We know that "celebrity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case celebrity = personality.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 PERSONALITY mean?
PERSONALITY noun- A set of non-physical psychological and social qualities that make a person (or thing) distinct from another.
- An assumed role or manner of behavior.
- A celebrity.
- Charisma, or qualities that make a person stand out from the crowd.
- Something said or written which refers to the person, conduct, etc., of some individual, especially something of a disparaging or offensive nature; personal remarks.
- That quality of a law which concerns the condition, state, and capacity of persons.