Seiryu was added in patch 4.5 of the Stormblood expansion.
Seiryu becomes available at level 70 as part of the “Surpassing the Samurai” quest, which is given by Bunchin – The Ruby Sea (X:27, Y:16).
The trial has a minimum ilevel of 365 to enter and rewards you with:
Allagan Tomestone of Poetics: 15