In contest, he taunted Greek character (5)
I believe the answer is:
theta
'greek character' is the definition.
(letter from the Greek alphabet)
'in contest he taunted' is the wordplay.
'in' indicates the answer is hidden within the clue.
'THETA' is hidden in the letters of 'contest he taunted'.
(Other definitions for theta that I've seen before include "letter from Athens" , "Character from overseas" , "8th letter of the Greek alphabet" , "character in Marathon" , "Letter to the Corinthians" .)