Celebrity in sergeants' mess (9)
I believe the answer is:
greatness
'celebrity' is the definition.
(I've seen this before)
'sergeants' mess' is the wordplay.
'mess' indicates an anagram.
'sergeants' with letters rearranged gives 'GREATNESS'.
'in' acts as a link.
(Other definitions for greatness that I've seen before include "''Some achieve ..., and some have ... thrust upon ?em'' (Twelfth Night)" , "Some achieve it; it's thrust upon others" , "Malvolio wasn't to fear being thrust into?" , "Immensity" , "Natal attribute or achievement or something thrust upon one!" .)