Mature way of working upset Greek character (5)
I believe the answer is:
omega
'greek character' is the definition.
(letter from the Greek alphabet)
'mature way of working upset' is the wordplay.
'mature' becomes 'age' ('age' can be a synonym of 'mature').
'way of working' becomes 'mo' (I've seen this in other clues).
'upset' says the letters should be written in reverse.
'age'+'mo'='agemo'
'agemo' in reverse letter order is 'OMEGA'.
(Other definitions for omega that I've seen before include "Last (Gk. letter)" , "Final outcome" , "letter to Greeks" , "16 letter" , "Final Greek letter" .)