Greek character — can't he take part? (5)
I believe the answer is:
theta
'greek character' is the definition.
(letter from the Greek alphabet)
'can't he take part?' is the wordplay.
'part?' says the answer is hidden in the clue.
'THETA' is hidden in the letters of 'cant he take'.
(Other definitions for theta that I've seen before include "Greek character" , "letter to Greeks" , "Foreign letter" , "Letter from Greece" , "character in Marathon" .)