Back to White Orchard
The Faithful Friend quest is only available during the final main quest of the game, Something Ends, Something Begins. This quest is also only available if you choose the Empress Ending where Ciri returns to Nilfgaard to take the throne.
When you leave the White Orchard Inn you’ll notice a horse throwing off a rider and bolting away. Chase after the horse and it will lead you to a Temerian Soldier. He’s the real owner of the horse and gave it to his friend to look after while he was away.
The soldier will reward you with a token and then ride off with the horse.