Pains gripping sick old Greek (8)
I believe the answer is:
achilles
'old greek' is the definition.
'pains gripping sick' is the wordplay.
'pains' becomes 'aches' (ache is a kind of pain).
'gripping' is an insertion indicator.
'sick' becomes 'ill' ('ill' can be a synonym of 'sick').
'aches' placed around 'ill' is 'ACHILLES'.
(Other definitions for achilles that I've seen before include "Famous Greek" , "Heroic warrior" , "Warrior of old" , "Greek warrior (with vulnerable heel)" , "man with a particular weakness" .)