Regalia of the High Priest is one of the new Class Order Hall sets coming in Legion. Unlike many armor sets in recent expansions, this set has 8 pieces with unique set bonuses for 2, 4, 6, and all 8 pieces. This is reminiscent of the earliest armor sets from Vanilla (e.g.Beastmaster Armor).
Many of these sets are recolors/variants of the Mists of Pandaria Challenge Mode armor sets.
As per current information, these sets start at an item level of 810, but can be upgraded to 820, 830 and 840. Note that these are entry-level sets, and are distinct from Tier 19 sets (which are ilvl 875 at Normal difficulty).
Each piece is obtained in a distinct way; what follows is a summary of each piece:
Helm: Order Hall quest.
Shoulders: Obtain Exalted reputation with The Nightfallen faction.
Chest: Complete your Class Order Campaign.
Wrists: Recruit 6 Champions for Order Hall.
Gloves: Obtain Honored reputation with The Nightfallen faction.
Belt: Earn 100,000 Artifact Power.
Leggings: Obtain Revered reputation with any 3 Broken Isles factions.
Feet: Defeat the final boss of every Legion Dungeon (any difficulty).