Adrian teleported to the Eastern Continent in search for the lost soul of the eastern rider. He does not know if he will find it intact and hopes that it has not dissipated. If he really wanted to then he could just get a random soul here and present it to the other riders.
The place where the eastern rider fell in battle is located at the northern part of the eastern continent. It is under the territory of the Xuan Wu which means he needs to be stealthy. Among the Four Divine Beasts of the Eastern Continent, the Xuan Wu or the Black Tortoise.
The Xuan Wu is also called the Divine Beast of the Frigid North. It has peak elemental affinity with water and is said to have mastered ice as well. Even Adrian will not be able to block an attack from a divine beast of that caliber unless he has an aid of another divine beast.