First ride on a new horse (4)
I believe the answer is:
roan
'horse' is the definition.
(roan is a kind of horse)
'first ride on a new' is the wordplay.
'first' indicates taking the first letters.
'a new' becomes 'an' (I've seen this in other clues).
The first letters of 'ride on' is 'ro'.
'ro'+'an'='ROAN'
(Other definitions for roan that I've seen before include "Red-coloured horse" , "Nora (anag) - horse" , "Bay spotted" , "(Horse) white-sprinkled coat" , "Horse with reddish-brown coat" .)