Greek character is out tracing Achaean origins (4)
I believe the answer is:
iota
'greek character' is the definition.
(letter from the Greek alphabet)
'is out tracing achaean origins' is the wordplay.
'origins' says to take the initial letters.
The initial letters of 'is out tracing achaean' is 'IOTA'.
(Other definitions for iota that I've seen before include "Contrivance" , "Tiniest scrap" , "Old letter" , "Smidgen" , "Greek letter; tiny amount" .)