It’s a man’s extraordinary staying power (7)
I believe the answer is:
stamina
'staying power' is the definition.
('stamina' can be a synonym of 'staying power')
'it's a man's extraordinary' is the wordplay.
'extraordinary' is an anagram indicator.
'its'+'a'+'man'='itsaman'
'itsaman' is an anagram of 'STAMINA'.
(Other definitions for stamina that I've seen before include "Ability to keep going" , "bottom" , "Indefatigability" , "Endurance, strength to stay the course" , "Parts of flowers" .)