Old giant, Greek character (5)
I believe the answer is:
omega
'greek character' is the definition.
(letter from the Greek alphabet)
'old giant' is the wordplay.
'old' becomes 'o' (abbreviation).
'giant' becomes 'mega' (mega means very big).
'o'+'mega'='OMEGA'
(Other definitions for omega that I've seen before include "completes a series" , "letter from abroad" , "Consummation" , "Foreign character" , "symbol of resistance?" .)