This new material can be found in Fleet Arena Shipments and Fleet Commander Events. A list of characters that have new levels of abilities requiring Zeta materials (and other components) were posted in the 11/21 Game Update, but here's a more in depth breakdown of what to expect.
Asajj Ventress
Nightsister Swiftness - Level 82
+25% Turn Meter Reduction Chance, +10% Turn Meter Reduction, Nightsisters gain 50% Turn Meter when they fall below 100% Health
Rampage - Level 84
Turn Meter Gain Chance +100%, +15% Turn Meter Gain, Buff Duration + 1
Barriss Offee
Swift Recovery - Level 82
Whenever an ally is Critically Hit they recover 20% of their Max Health
Captain Phasma
Fire at Will - Level 82
-15% Damage Penalty, triple Assist chance for First Order, and First Order allies gain 20% Potency
CC-2224 "Cody"
Ghost Company Commander - Level 82
+5% Critical Chance, +10% Defense, and Clone allies recover 5% of their Max Protection whenever they use a Basic ability
Clone Wars Chewbacca
Defiant Roar - Level 82
+25% Turn Meter Gain Chance, +10% Heal, and dispel all debuffs from self
CT-5555 "Fives"
Tactical Awareness - Level 82
Fives gains 15% Turn Meter whenever another Clone ally takes damage and 7.5% Turn Meter whenever a non-Clone ally takes damage
Darth Maul
Dancing Shadows-Level 82
Sith allies gain Stealth for 1 turn on Evade, can't be Critically Hit while Stealthed, gain Advantage for 2 turns whenever Stealth expires, and gain all "on Evade" bonuses at the start of each encounter
Darth Sidious
Sadistic Glee - Level 82
100% Turn Meter Gain Chance, +50% Potency, and gain Max Health equal to Potency percentage
Darth Vader
Inspiring Through Fear - Level 82
+25% Turn Meter Reduction Chance, +10% Turn Meter Reduction, enemies immediately regain Damage Over Time for 2 turns whenever Damage Over Time expires on them while Darth Vader is alive
Grand Master Yoda
Grand Master's Guidance - Level 82
+5% Tenacity, +5% Turn Meter Gain, and whenever a Jedi ally suffers a debuff they gain Tenacity Up for 1 turn at the end of that turn
Grand Master Yoda
Battle Meditation - Level 84
Cooldown - 1 and gain Foresight for 2 turns
Luminara Unduli
Elegant Steps - Level 82
+2% Heal and whenever any ally gains a buff they do not have, they gain a Heal Over Time effect for 2 turns
Qui-Gon Jinn
Agility Training - Level 82
+5 Speed, Jedi allies gain Offense equal to 3 times their Speed, and gain Foresight for 2 turns at the start of each encounter and whenever any unit is defeated
Rey
Focused Strikes - Level 82
Whenever Rey uses a Special ability, if she has no debuffs, she inflicts Daze for 2 turns which can't be Resisted
Additional Notes
General
Fixed the text in the Fleet Mega-Pack description to accurately represent the correct drop rate.
All Thermal Detonator abilities now gain bonus potency based on the Damage stats of the character.
Asajj Ventress
Updated description of "Nightsister Swiftness" to correctly indicate that the Turn Meter removal can't be resisted.
"Rampage" now grants Asajj 15 Speed for each enemy with no buffs.
Barriss Offee
"Swift Recovery" has been reworked to dispel all debuffs from the lowest health ally.
CC-2224 "Cody"
Clone allies now gain half of the Defense Cody gains from "Ghost Company Commander."
Darth Maul
"Whirling Blades" now inflicts Daze for 2 turns.
"Power of Hatred" Omega Upgrade now grants +20% Max Health, gain Max Health equal to 10% of damage dealt, and Potency equal to 0.3% of Max Health, in addition to previous bonuses.
"Dancing Shadows" now grants Turn Meter when Critically Hit in addition to when Evading.
Replies
Asajj Ventress
Nightsister Swiftness - Level 82
+25% Turn Meter Reduction Chance, +10% Turn Meter Reduction, Nightsisters gain 50% Turn Meter when they fall below 100% Health
Rampage - Level 84
Turn Meter Gain Chance +100%, +15% Turn Meter Gain, Buff Duration + 1
Barriss Offee
Swift Recovery - Level 82
Whenever an ally is Critically Hit they recover 20% of their Max Health
Captain Phasma
Fire at Will - Level 82
-15% Damage Penalty, triple Assist chance for First Order, and First Order allies gain 20% Potency
CC-2224 "Cody"
Ghost Company Commander - Level 82
+5% Critical Chance, +10% Defense, and Clone allies recover 5% of their Max Protection whenever they use a Basic ability
Clone Wars Chewbacca
Defiant Roar - Level 82
+25% Turn Meter Gain Chance, +10% Heal, and dispel all debuffs from self
CT-5555 "Fives"
Tactical Awareness - Level 82
Fives gains 15% Turn Meter whenever another Clone ally takes damage and 7.5% Turn Meter whenever a non-Clone ally takes damage
Darth Maul
Dancing Shadows-Level 82
Sith allies gain Stealth for 1 turn on Evade, can't be Critically Hit while Stealthed, gain Advantage for 2 turns whenever Stealth expires, and gain all "on Evade" bonuses at the start of each encounter
Darth Sidious
Sadistic Glee - Level 82
100% Turn Meter Gain Chance, +50% Potency, and gain Max Health equal to Potency percentage
Darth Vader
Inspiring Through Fear - Level 82
+25% Turn Meter Reduction Chance, +10% Turn Meter Reduction, enemies immediately regain Damage Over Time for 2 turns whenever Damage Over Time expires on them while Darth Vader is alive
Grand Master Yoda
Grand Master's Guidance - Level 82
+5% Tenacity, +5% Turn Meter Gain, and whenever a Jedi ally suffers a debuff they gain Tenacity Up for 1 turn at the end of that turn
Grand Master Yoda
Battle Meditation - Level 84
Cooldown - 1 and gain Foresight for 2 turns
Luminara Unduli
Elegant Steps - Level 82
+2% Heal and whenever any ally gains a buff they do not have, they gain a Heal Over Time effect for 2 turns
Qui-Gon Jinn
Agility Training - Level 82
+5 Speed, Jedi allies gain Offense equal to 3 times their Speed, and gain Foresight for 2 turns at the start of each encounter and whenever any unit is defeated
Rey
Focused Strikes - Level 82
Whenever Rey uses a Special ability, if she has no debuffs, she inflicts Daze for 2 turns which can't be Resisted
Additional Notes
General
Fixed the text in the Fleet Mega-Pack description to accurately represent the correct drop rate.
All Thermal Detonator abilities now gain bonus potency based on the Damage stats of the character.
Asajj Ventress
Updated description of "Nightsister Swiftness" to correctly indicate that the Turn Meter removal can't be resisted.
"Rampage" now grants Asajj 15 Speed for each enemy with no buffs.
Barriss Offee
"Swift Recovery" has been reworked to dispel all debuffs from the lowest health ally.
CC-2224 "Cody"
Clone allies now gain half of the Defense Cody gains from "Ghost Company Commander."
Darth Maul
"Whirling Blades" now inflicts Daze for 2 turns.
"Power of Hatred" Omega Upgrade now grants +20% Max Health, gain Max Health equal to 10% of damage dealt, and Potency equal to 0.3% of Max Health, in addition to previous bonuses.
"Dancing Shadows" now grants Turn Meter when Critically Hit in addition to when Evading.