Greek philosopher half ignored old Roman god (5)
I believe the answer is:
pluto
'roman god' is the definition.
(god of the underworld)
'greek philosopher half ignored old' is the wordplay.
'greek philosopher' becomes 'Plutarch' (ancient Greek philosopher).
'half ignored' means to take half the letters.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'plutarch' cut in half is 'plut'.
'plut'+'o'='PLUTO'
(Other definitions for pluto that I've seen before include "Roman god" , "Dis" , "animated dog" , "wartime acronym" , "Solar system body" .)