Celebrity on edge (6)
I believe the answer is:
legend
'celebrity' is the definition.
(both can mean a renowned person)
'on edge' is the wordplay.
'on' becomes 'leg' (cricket term, fielding positions).
'edge' becomes 'end' (I've seen this in other clues).
'leg'+'end'='LEGEND'
(Other definitions for legend that I've seen before include "Motto" , "Tale; caption" , "Traditional story; caption" , "Story from long ago" , "Story of mythical beings or events" .)