A celebrity may have one (4)
I believe the answer is:
aura
'a celebrity may have one' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for aura that I've seen before include "Distinctive character, essence of a living thing" , "Intangible air or quality" , "Perception of distinctive personality" , "Invisible emanation" , "Distinctive quality (of something or someone)" .)