The new priest trinket drops from Archimonde, the last boss in HFC. I've been playing a bit with it, and these are my impressions so far:
For shadow, the trinket places a stacking debuff on the target, which increases the damage taken from your mind spells by 3.29% per stack: Mind Spike, Mind Blast, Mind Flay, and Insanity. (Mind Sear is currently not being affected by Mental Fatigue).
With AS, the trinket debuff is refreshed naturally while playing AS as usual on a single target fight, the problem is that as the number of targets increases, you get less MF uptime, and since Mental Fatigue is a debuff placed on the target, you'll have to switch targets constantly to keep the debuff up on more than one target.
With CoP, it looks like haste breakpoints are back. We'll likely start the fight building up Mental Fatigue stacks (with an even worse burst on pull than usual because of this), and after that you need at least 1 tic of MF every 10 seconds to keep the debuff up, so you'll want to have enough haste (easily attainable with t18 gear) to go through a (MSpx3 + MB + MSpx2 + MF) cycle in under 10 seconds. Otherwise you'll have to replace every 5th Mind Spike with a Mind Flay to keep Mental Fatigue up, which while still higher dps than not keeping Mental Fatigue up at all, is lower than replacing one in six spikes with a MF, and makes up for a much clunkier rotation.
With Void Entropy, it's awesome. Everything is awesome. It's fun, it's engaging, it's powerful, I'm taking it for every single fight now. </sarcasm>
For Holy, while in Chakra: Sanctuary, it increases the cast time and mana cost of Heal by 49% and increases its healing by 99%. I.e., it pretty much turns Heal into Greater Heal, our long lost big slow heal which has had no use since the beginning of Cataclysm. I honestly can't picture myself needing to use it with the current healing mechanics.
For Disc, your Penance, Flash Heal, Heal, and Prayer of Healing also grant Naaru's Discipline to allies, reducing damage taken by X% for 10 sec. I haven't played disc since WoD started and I don't intend to, so I haven't played with this. The damage reduction looks like a nice perk though.