Argives initially invading pain an old Greek (7)
I believe the answer is:
achaean
'old greek' is the definition.
(person from Achaea in Greece in ancient times)
'argives initially invading pain an' is the wordplay.
'initially' suggests taking the first letters.
'invading' indicates putting letters inside.
'pain' becomes 'ache' (ache is a kind of pain).
The first letter of 'argives' is 'a'.
'a' going into 'ache' is 'achae'.
'achae'+'an'='ACHAEAN'
(Other definitions for achaean that I've seen before include "Ancient Greek" , "provincial Greek" , "about ancient Greeks" .)