The most common and most likely answer to this crossword clue is the 11 letter word DISTINCTION
I've seen this crossword clue in The Guardian
D
I
S
T
I
N
C
T
I
O
N
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 = distinction.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 DISTINCTION mean?
DISTINCTION noun- That which distinguishes; a single occurrence of a determining factor or feature, the fact of being divided; separation, discrimination.
- The act of distinguishing, discriminating; discrimination.
- Specifically, a feature that causes someone or something to stand out as being better; a mark of honour, rank, eminence or excellence; being distinguished.