He enters races with a foreign character (5)
I believe the answer is:
theta
'foreign character' is the definition.
(Greek letter)
'he enters races with a' is the wordplay.
'enters' indicates putting letters inside.
'races' becomes 'tt' (Isle of Man Tourist Trophy races).
'with' is a charade indicator (letters next to each other).
'he' going within 'tt' is 'thet'.
'thet'+'a'='THETA'
(Other definitions for theta that I've seen before include "Letter from Greece" , "Greek letter used in trigonometry" , "Letter before iota" , "classic character?" , "Greek letter equivalent to th" .)