Celebrity's naked? Not half! (4)
I believe the answer is:
star
'celebrity's' is the definition.
(thesaurus)
'naked? not half' is the wordplay.
'naked?' becomes 'starkers' (I've seen this before).
'not half' means to take half the letters.
'starkers' halved is 'STAR'.
(Other definitions for star that I've seen before include "A night light?" , "Celeb" , "Leading character" , "Five- or six-pointed figure" , "Famous performer" .)