This WoW set features the full Avatar transmog, which is the priest tier 5 raid set. Avatar is obtained by looting armor tokens from various Burning Crusade bosses. These tokens can be traded for set pieces via Shattrath City tier vendors.
How to Get Priest Tier 5? By slaying Serpentshrine Cavern and The Eye (Tempest Keep) bosses.
Are There Multiple Tier 5 Transmogs For My Class? No, some classes do have multiple tier 5 sets (depending on their class trees), but every tier set variation features the same exact transmog look. For example, the paladin has a different set for retribution, holy, and protection, but all three sets share the same exact model and color variation. (Hunter, Mage, Rogue, and Warlock feature only one tier 5 set)
How Many Set Pieces?  Helmet, Shoulders, Chest, Hands, and Pants
Priest Tier 5 Transmog: [Drop Locations]
Note: Priest have two different sets with the same exact look. Tier 5 priest armor tokens can be used to purchase any of the set pieces.
Head: Helm of the Vanquished Defender by slaying Lady Vashj in Serpentshrine Cavern.
Chest: Chestguard of the Vanquished Defender by slaying Kael’thas Sunstrider in The Eye.
Hands: Gloves of the Vanquished Defender by slaying Leotheras the Blind in Serpentshrine.
Legs: Leggings of the Vanquished Defender by slaying Fathom-Lord Karathress in Serpentshrine.
Tier 5 Set Vendors: [24,27] Kelara (Aldor) OR [44,91] Veynna Dawnstar (Scryer) | ~Shattrath City~
Set Name: Avatar Raiment (hover for set bonuses)
Shoulder: Mantle of the Avatar
Chest: Vestments of the Avatar
Hands: Gloves of the Avatar
Legs: Breeches of the Avatar