Noted horse for a master intellectual (7)
I believe the answer is:
egghead
'intellectual' is the definition.
(I know that egghead is a type of intellectual)
'noted horse for a master' is the wordplay.
I cannot really see how this works, but
'horse' could be 'gg' (geegee or GG is a childish term for a horse) and 'gg' is found within the answer.
'a' is found in the answer.
The remaining letters 'ehed' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for egghead that I've seen before include "Brainiac" , "Intellectual, studious academic" , "brain" , "Very academic person" , "An intellectual (inf.)" .)