Celeb ultimately craves that extra honour (4)
I believe the answer is:
star
'celeb' is the definition.
(I've seen this in another clue)
'ultimately craves that extra honour' is the wordplay.
'ultimately' suggests the final letters.
The final letters of 'craves that extra honour' are 'STAR'.
(Other definitions for star that I've seen before include "Point of light in the heavens" , "A .... called Henry (Roddy Doyle)" , "E.g.Sirius" , "Brilliant person" , "Glamorous celebrity" .)