Horse in flat race, not Ascot's first (7)
I believe the answer is:
eventer
'horse' is the definition.
(I have seen 'Equestrian horse ' mean 'eventer' so perhaps 'horse' could also mean 'eventer')
'flat race not ascot's first' is the wordplay.
I cannot really see how this works, but
'flat' could be 'even' ('even' can be similar in meaning to 'flat') and 'even' is located in the answer.
This may be the basis of clue (or it may be nonsense).
'in' acts as a link.
Can you help me to learn more?
(Other definitions for eventer that I've seen before include "Sportsman" , "Jumper" , "Rider in contests" , "Competing horse or rider" , "versatile horse" .)