Horse moves long time after groom (8)
I believe the answer is:
dressage
'horse moves' is the definition.
(equestrian sport)
'long time after groom' is the wordplay.
'long time' becomes 'age' (an age is a period of time).
'after' is a charade indicator (letters next to each other).
'groom' becomes 'dress' (synonyms).
'age' after 'dress' is 'DRESSAGE'.
(Other definitions for dressage that I've seen before include "Art of horse training" , "Equestrian sport of manoeuvring" , "Event for rider" , "Olympic event" , "Red gases (anag)" .)