A type of racing person goes after class at American university after dropping Charlie (7,3)
I believe the answer is:
formula one
'a type of racing person goes after class' is the definition.
I know nothing about this answer so I cannot judge whether this works.
'american university after dropping charlie' is the wordplay.
'american university' becomes 'formula' (I can't justify this - if you can you should give a lot more credence to this answer).
'after' becomes 'once' (once can mean immediately after).
'dropping' indicates named letters should be taken away.
'charlie' becomes 'c' (phonetic alphabet: alpha, bravo, charlie etc.).
'once' with 'c' taken out is 'one'.
'formula'+'one'='FORMULA ONE'
'at' is the link.
Can you help me to learn more?
(Other definitions for formula one that I've seen before include "Auto racing class" , "sort of GP" .)