Reveal support for riding style (8)
I believe the answer is:
bareback
'riding style' is the definition.
'reveal support' is the wordplay.
'reveal' becomes 'bare'.
'support' becomes 'back' (back is a kind of support**).
'bare'+'back'='BAREBACK'
'for' is the link.
(Other definitions for bareback that I've seen before include "On an unsaddled horse" , "On a horse without a saddle" , "kind of riding" .)