Celebrity should be about at this time, either side of noon (6)
I believe the answer is:
renown
'celebrity' is the definition.
(I know that celebrity can be written as renown)
'about at this time either side of noon' is the wordplay.
'about' becomes 're' (regarding).
'at this time' becomes 'now' (at the present time).
'either side of' says to take the initial letters (the first and last letters are the same).
The first letter of 'noon' is 'n'.
're'+'now'+'n'='RENOWN'
'should be' is the link.
(Other definitions for renown that I've seen before include "Fame, respect" , "High repute" , "Plane's maximum width" , "Fame and distinction" , "Fame and public acclamation" .)