Greek character notes Catholic dignitary’s top position (8)
I believe the answer is:
chiefdom
'top position' is the definition.
(I've seen this before)
'greek character notes catholic dignitary's' is the wordplay.
'greek character' becomes 'chi' (letter from the Greek alphabet).
'notes' becomes 'ef'.
'catholic dignitary' becomes 'dom' (title for some Catholic monks, from Latin dominus).
'chi'+'ef'+'dom'='CHIEFDOM'
(Other definitions for chiefdom that I've seen before include "Top position" , "State of being a leader" , "Head position in a clan" .)