Dragonspire Hall is an area of Upper Blackrock Spire. It is accessed through the sealed door in the Hall of Blackhand. Once one had to be in the possession of the Seal of Ascension to open it, but this is no longer required.
The hall is the first area where a 10-man group is recommended if the group is level 60. To access the next area, the Hall of Binding where Pyroguard Emberseer is located, one must defeat every single orc in this area.