So, the four new CSM psychic disciplines in Traitors Hate turn out to be actually the same as what Space Marines received in Angels of Death, only with different names and fluff.
Based on all that, here is my initial take on how some of these powers can be integrated into a competitive CSM army:
 “Fleshmetal Hide” on Nurgle Biker Lord/Nurgle Bikers — Nurgle Bikers are T6 already, then you cast Fleshmetal Hide on them and they become T7, which is better than most MCs! Imagine a squad of these Bikers with a Nurgle Biker Lord (or two) attached… if they Jink, it would take an average of 27 x BS4 Bolter shots or 6 BS4 Plasma shots to cause a single Unsaved Wound on this unit. Additionally, in close combat, S4 attacks would only wound them on a 6+ and even S8 PFs would only wound them on a 3+. Finally, T7 makes the Chaos Biker Lord(s) basically immune to Instant Death (except from Force Weapons) and means they can easily shrug off some of the toughest enemy attacks in the game. Putting it all together, I think Nurgle Bikers/Lords with Fleshmetal hide cast on them is an ideal way to deliver a powerful close combat unit into enemy lines and then wreck havoc there without requiring lots of outside support/assistance.
 Ahriman in a Kharybdis Assault Claw with “Electromortis” and/or “Daemon Shriek” — Drop Ahriman and his attached squad in Turn 1 in the middle of a large quantity of enemy vehicles (say, an Astra Militarum mech force or a Space Marine Battle Company with lots of Rhinos/Razorbacks). Then cast Electromortis (18″ Haywire Beam) or Daemon Shriek (9″ Haywire Nova) three times in a row… this will likely remove all or most HPs from the targeted enemy vehicles in a single “volley” and clear out a significant portion of their mech forces. If the enemy runs out of vehicles to target, then Ahriman can switch to Psychic Shriek and use that multiple times a turn to deal with tough infantry/MCs.
 Possessed and “Soul Switch” — The key problem with Possessed is getting them into combat successfully (once there, they are pretty potent). Infiltrate (from Master of Deception WL Trait) a friendly Bike/Beast/Jump Infantry unit within 18″ of the enemy, then Turn 1 move that unit up 12″ so that it is within 6″ of the enemy you are looking to charge with the Possessed. Then, in the Psychic Phase, use Soul Switch to “swap” your friendly unit with a unit of Possessed and their attached Sorcerer, followed by a 6″ charge in the assault phase. While not 100% (especially if the enemy has a turn to shoot at the infiltrated unit first), this is a great way to get Possessed into combat Turn 1, where they can really shine (especially if they are part of the new Favored of Chaos formation and get access to all three mutations at once if their Daemon Prince is within 12″).
 “Ley Leech” and Winged Nurgle Daemon Princes — With T5 and Jink/Shrouded already, Flying Nurgle DPs are already quite difficult to deal with. Add in IWND and the ability to restore D3 wound each Psychic Phase from Ley Leech and these MCs become even more durable. Better yet, if they do not need to cast Ley Leech on themselves, then they can cast it on a friendly unit within 18″, giving you plenty of flexibility in keeping your multi-wound characters alive.
 Predator Squadrons and “Earthly Anathema” — With their newly found ability to squadron in units of 1-3 tanks (and gain Tank Hunter/Monster Hunter if they have 3 tanks), Chaos Predators are now on par with their Loyalist counterparts. Add to this the Psychic Power “Earthly Anathema” and they also gain Move through Cover, Ignore Cover for their shooting, and the ability to shoot at targets that they do not have LOS to. With 3 Triple Lascannon Predators, this makes them especially deadly against enemy tanks, MCs, infantry, and even flyers (in a pinch), since that is 9 x S9 AP2 shots at 48″ with Ignore Cover and Tank Hunter/Monster Hunter “built-in.”
 Tzeentch Terminators and “Warp Fate” — While generally not considered very competitive right now, Tzeentch Terminators do have solid survivability with their 2+/4++. If you cast Warp Fate on them, that means they can re-roll all their saves, which translates to a 97% survivability rate against non-AP2/1 attacks and a 75% survivability rate against AP2/1 weapons. Those are very solid stats, especially if you combine them with the new rules for the Terminator Annihilation Force, which gives Hatred and bonus shooting options against selected enemy units, making these Chaos Terminators not only more durable, but put out more combat power as well, thereby measurably increasing their value within your army.
 Plasma Chosen with “Death Hex” — Since Chosen squads can take up to 5 Plasma guns, plus 1 Plasma Pistol, they are one of the better CSM counters to heavy infantry/MCs. Combine this with a mobile deliver system (like a Rhino) and then cast Death Hex on their target, for a -2 to the target’s Invul save, and they can quickly become devastating to Stormsurges, Riptides, Loyalist Hammernators, Necron Wraiths, Eldar Farseers/Warlocks, TWC with Storm Shields, and basically any elite enemy units that rely heavily on Invul saves. This combines particularly well with “The Ravagers” formation from the Crimson Slaughter supplement, which gives free re-rolls to Hit each turn as long as the Chosen Champion is still alive.
 Chaos Knight with “Earthly Anathema” and/or “Fleshmetal Hide” — Now that CSM have “formal” access to Renegade Knights (via the Forsworn Knight Detachment) as allies, this opens up lots of options for them. In particular, unlike their Imperium counterparts, Renegade Knights have the ability to take “double” shooting weapons (i.e. two Thermal Cannons, two Avenger Gatling cannons, etc.) in addition to the normal Carapace Weapon options. This makes them exceptional candidates for the “Earthly Anathema” power, since they can shoot at up to three different targets per turn with powerful weapons, Ignore Cover, and the ability to ignore LOS restrictions (i.e. a Renegade Knight with two Avenger Gatling Cannons and a Stormspear Rocket Pod, plus “Earthly Anathema” cast on it, could easily kill three separate Eldar Jetbike squads a turn). Additionally, being highly durable Super-Heavy Walkers, Renegade Knights benefit significantly from “Fleshmetal Hide,” since that increases their protection to AV14/13/13, making it significantly more difficult to destroy them.
While there are many other potential combinations, I think some of these that I have listed above will find their way into competitive Chaos Space Marine lists, especially as they provide so much flexibility and tactical options that CSM have generally lacked in the last couple of years.