The most common and most likely answer to this crossword clue is the 12 letter word SUPERSTARDOM
I've seen this crossword clue in The Times
S
U
P
E
R
S
T
A
R
D
O
M
Buddy explains!

The straight part
We know that "Major celebrity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case major celebrity = superstardom.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 SUPERSTARDOM mean?
SUPERSTARDOM noun- The status or position of a superstar.