Horse initially noted at Goodwood (3)
I believe the answer is:
'horse' is the definition.
(term for an old horse)
'initially noted at goodwood' is the wordplay.
'initially' indicates taking the first letters.
The first letters of 'noted at goodwood' is 'NAG'.
(Other definitions for nag that I've seen before include "Harry", "Termagant", "Old horse or shrewish wife", "Annoy constantly", "Old or over-worked horse".)