Apprentice's exhausted tutor coming to the fore in racecourse (7)
I believe the answer is:
trainee
'apprentice's' is the definition.
(someone undergoing training)
'exhausted tutor coming to the fore in racecourse' is the wordplay.
'exhausted' says to hollow out the word (remove centre letters) (the word is emptied out or exhausted).
'coming to' is a charade indicator (letters next to each other).
'the fore in racecourse' becomes 'ainee' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'tutor' with its middle removed is 'tr'.
'tr'+'ainee'='TRAINEE'
Can you help me to learn more?
(Other definitions for trainee that I've seen before include "novice" , "Person under instruction" , "Person being instructed in work" , "One being taught a job" , "one not yet qualified" .)