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' is an anagram of 'GREATNESS'.
'in' is the 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!" .)