Greek character is out to avenge, first of all (4)
I believe the answer is:
iota
'greek character' is the definition.
(letter from the Greek alphabet)
'is out to avenge first of all' is the wordplay.
'first of all' suggests taking the first letters.
The first letters of 'is out to avenge' is 'IOTA'.
(Other definitions for iota that I've seen before include "Just a jot, like Greek letter" , "The smallest possible amount, or the Greek i" , "Ninth letter of Greek alphabet, small amount" , "Smidgen" , "very small part" .)