The task is halved with this Greek character (5)
I believe the answer is:
theta
'this greek character' is the definition.
(letter of the Greek alphabet)
'the task is halved' is the wordplay.
'is halved' suggests halving the letters.
'task' halved is 'ta'.
'the'+'ta'='THETA'
'with' is the link.
(Other definitions for theta that I've seen before include "character in Marathon" , "classic character?" , "Letter before iota" , "Character from overseas" , "Eighth letter of Greek alphabet" .)