Longs to nurse poorly Greek hero (8)
I believe the answer is:
achilles
'greek hero' is the definition.
(I've seen this before)
'longs to nurse poorly' is the wordplay.
'longs' becomes 'aches' ('ache' can be a synonym of 'long').
'to nurse' is an insertion indicator.
'poorly' becomes 'ill' ('ill' can be a synonym of 'poorly').
'aches' enclosing 'ill' is 'ACHILLES'.
(Other definitions for achilles that I've seen before include "man with a particular weakness" , "Heroic Greek with damaged heel" , "Warrior of old" , "Mythical hero, vulnerable only through his heel" , "His heel was his weak point" .)