Celebrity beginning without ending (4)

I believe the answer is:

star

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'celebrity' is the definition.
(a star is a celebrity or famous person)

I don't understand the remainder of the clue.

(Other definitions for star that I've seen before include "Famous actor" , "Shiner" , "Ball of fire" , "White blaze on a horse's forehead" , "Eg, Betelgeuse" .)

I've seen this clue in The Times.

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