Celebrity's unavailability — not at home (4)

I believe the answer is:

fame

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'celebrity's' is the definition.
('fame' can be a synonym of 'celebrity')

I can't explain the rest of the clue.

(Other definitions for fame that I've seen before include "Renown, celebrity" , "''... is the spur that the clear spirit doth raise (Lycidas, John Milton)" , "Notoriety or celebrity" , "Musical - stardom" , "Prominence" .)

I've seen this clue in The Times.

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