Groom to get on as horse moves (8)
I believe the answer is:
dressage
'horse moves' is the definition.
(equestrian sport)
'groom to get on' is the wordplay.
'groom' becomes 'dress' (dressing is a kind of grooming).
'to get on' becomes 'age' ('age' can be a synonym of 'get on').
'dress'+'age'='DRESSAGE'
'as' is the link.
(Other definitions for dressage that I've seen before include "discipline for horses" , "Art of horse training" , "Equestrian manoeuvres" , "Training for competition" , "Equestrian performance" .)