Exposed tax-averse rider (4,6)
I believe the answer is:
lady godiva
'tax-averse rider' is the definition.
(Lady Godiva rode naked to protest taxation)
I cannot understand how the rest of the clue works.
(Other definitions for lady godiva that I've seen before include "Only Peeping Tom saw her ride!" , "Wife of Leofric, an early streaker!" , "Naked rider through Coventry" , "She rode bareback (and bare front!)" , "romantic comedy film" .)