Analytic (Porygon, Magnemite, Staryu, Elgyem, Patrat)
Aroma Veil (Spritzee)
Flare Boost (Drifloon)
Friend Guard (Scatterbug, Happiny, Cleffa, Igglybuff; note that Chansey/Clefable/Wigglytuff shift to a different ability instead)
Gale Wings (Fletchling)
Galvanize (Alola Geodude)
Gooey (Goomy)
Grass Pelt (Skiddo)
Harvest (Exeggcute, Phantump, Tropius)
Heavy Metal (Aron, Bronzor)
Imposter (Ditto)
Light Metal (Beldum, Registeel, Scizor)
Liquid Voice (Popplio)
Long Reach (Rowlet)
Moody (Smeargle, Bidoof, Remoraid, Snorunt)
Multiscale (Lugia, Dragonite)
Pickpocket (Sneasel, Seedot, Binacle)
Power of Alchemy (Alola Grimer)
Protean (Froakie, Kecleon)
Rattled (Alola Meowth, Snubbull, Bonsly, Dunsparce, and first-stage but not later stages for Magikarp, Poochyena, Whismur, Ledyba, Clamperl, and Cubchoo)
Symbiosis (Flabebe, and would also include Oranguru but there's no legal way to get Oranguru with that ability yet)
Toxic Boost (Zangoose)
Zen Mode (Darmanitan)