Race: The Great Erasmus Vegelbud Memorial Derby - Novigrad
Location: Hierarch Square - Vegelbud Residence
Quest Giver: Hierarch Square Notice on table
Other Requirements: N/A
You can start this quest any time after completing the Get Junior Story Quest. In the middle of Hierarch Square you'll find an announcer and a table next to him with a bunch of papers on it (pictured above). Loot an Invitation to the Memorial Derby off of the table and read it to begin this quest.
For the first part of this quest you'll need to travel over to the Vegelbud Residence where you'll want to speak with the Race Master (pictured below) to begin these horse races. Save before you decide to enter into any of the races as if you lose you won't get another opportunity to win them.
Each time you pay an entry fee you'll get 10 EXP. Winning a race will get you a unique item and a certain amount of Crowns depending on which number race it is but no EXP. All of the available rewards that you can win are mentioned below.
Reward #1: Superior Racing Saddle
Reward #2: Rugged Saddlebags
Reward #3: Superior Cavalry Saddle
These races for the most part aren't too difficult, if you're having trouble with them I would recommend doing the Velen or Skellige racing quests which will net you some upgrades for Roach (or visit the Hearts of Stone merchant in Upper Mill for the best upgrades). You could also wait until the Blood on the Battlefield Story Quest where you're gifted a black horse if you refuse the Emperor's gold reward.
Once you've won all three races a dwarf will meet you when you're trying to leave the area and give you a letter from Cleaver. Read it and he asks you to meet him in Novigrad, Cleaver's request is for you to race in his name in the Palio race. He plans to bet a lot of money on you so there is a sizable reward for winning.
Before you enter in this race it's recommended that you save your game, you're only going to get a single shot at winning. I've outlined the route that you will be following throughout the race below, you'll have to lay off the sprinting at some point to recover Roach's Stamina - when you do this try to have your opponents run into Roach's ass to slow them down.
Once the race is over and Cleaver either complains to you or gives you your reward the quest will complete. Also, a fight will break out amongst the people watching the horse race and the Temple Guards. It's recommended you just run away and leave everyone to die.