Ancient Wardstone: Centaur's Stand
This is a horse race... or, more specifically, a centaur race. Jerome Drift will give you a Centaur-transmogrification so you can compete in a race. The bell you need to ring is on the road at 8118, 6575.
If you do not have some kind of speed-increasing ability, potion, or skill you can probably not win. The other Centaur is just a little bit faster and no amount of corner-cutting is gonna shave enough extra seconds off this run. Be sure to apply your speed-increase before being transformed, but there is an NPC at the bell that can re-apply the spell if you need it.
-- UPDATE -- Not sure if this quest recently changed, but i did it without a speed potion. There are blue orbs on the floor that give you a burst of speed for like 5 secs (like the ones that buff you in warfronts). You shouldn't grab all though - pick strategically the ones that are on your way to the next marker. I was able to beat the runner by around 5 seconds.