Entertain a Greek goddess, one of nine (5)
I believe the answer is:
amuse
'entertain' is the definition.
(amusing is a kind of entertaining)
'a greek goddess one of nine' is the wordplay.
'greek goddess one of nine' becomes 'muse' (the nine muses of Greek myth).
'a'+'muse'='AMUSE'
(Other definitions for amuse that I've seen before include "Cause to laugh or smile" , "Divert or entertain mildly" , "Enliven" , "Make (someone) laugh" , "Reflect" .)