He enters races — a character from Greece (5)
I believe the answer is:
theta
'character from greece' is the definition.
(Greek letter)
'he enters races a' is the wordplay.
'enters' indicates putting letters inside.
'races' becomes 'tt' (Isle of Man Tourist Trophy races).
'he' put within 'tt' is 'thet'.
'thet'+'a'='THETA'
(Other definitions for theta that I've seen before include "Letter to the Corinthians" , "Homeric character" , "Letter from Greece" , "classic character?" , "Eighth letter of Greek alphabet" .)