Like most New Pokemon Games, Pokemon Ultra Sun includes brand new Egg Moves for loads of older Pokemon. For the most part, these new Egg Moves have been given to better aid the Pokemon with being more competitive. However, that being said, not all new Eggs Moves do that very thing for every given Pokemon.
New Egg Moves
Sandshrew, Alolan Sandshrew, Sandslash, Alolan Sandslash: Hone Claws
Oddish, Gloom, Vileplume, Bellossom: Strength Sap
Paras, Parasect: Grassy Terrain
Abra, Kadabra, Alakazam: Psychic Terrain
Bellsprout, Weepinbell, Victreebel: Strength Sap
Ponyta, Rapidash: High Horsepower
Farfetch'd: First Impression, Final Gambit
Grimer, Alolan Grimer, Muk, Alolan Muk: Power-Up Punch
Onix, Steelix: Wide Guard
Drowzee, Hypno: Power Split, Psychic Terrain
Cubone, Marowak, Alolan Marowak: Curse
Lickitung, Lickilicky: Thrash
Koffing, Weezing: Venom Drench
Tangela, Tangrowth: Wake-Up Slap
Mime Jr., Mr. Mime: Psychic Terrain
Snorlax: Power-Up Punch
Sentret, Furret: Baby-Doll Eyes
Hoothoot, Noctowl: Mean Look, Hurricane
Ledyba, Ledian: Endure, Counter
Spinarak, Ariados: Lunge
Hoppip, Skiploom, Jumpluff: Strength Sap
Aipom, Ambipom: Tail Slap
Wooper, Quagsire: Power-Up Punch
Murkrow, Honchkrow: Punishment
Girafarig: Psychic Terrain, Psychic Fangs
Delibird: Counter
Phanpy, Donphan: High Horsepower
Zigzagoon, Linoone: Extreme Speed
Whismur, Loudred, Exploud: Whirlwind
Mawile: Power-Up Punch
Plusle: Tearful Look
Minun: Tearful Look
Volbeat: Lunge
Illumise: Aromatherapy
Roselia, Roserade: Power Whip
Numel, Camerupt: Heavy Slam
Cacnea, Cacturne: Power-Up Punch
Swablu, Altaria: Play Rough
Zangoose: Belly Drum
Kecleon: Power-Up Punch
Tropius: Dragon Hammer
Chimecho: Crafty Shield, Perish Song
Turtwig, Grotle, Torterra: Heavy Slam
Chimchar, Monferno, Infernape: Power-Up Punch
Piplup, Prinplup, Empoleon: Power Trip
Bidoor, Bibarel: Mud Sport
Pachirisu: Baby-Doll Eyes
Buizel, Floatzel: Helping Hand
Cherubi, Cherrim: Grassy Terrain
Buneary, Lopunny: Power-Up Punch
Spiritomb: Disable
Riolu, Lucario: Meteor Mash
Carnivine: Acid Spray
Finneon, Lumineon: Confuse Ray
Tepig, Pignite, Emboar: Burn Up
Oshawott, Dewott, Samurott: Sacred Sword
Patrat, Watchog: Tearful Look, Bullet Seed
Pansage, Simisage: Spiky Shield
Pansear, Simisear: Belch, Flare Blitz
Blitzle, Zebstrika: Feint
Timburr, Gurdurr, Conkeldurr: Power-Up Punch
Tympole, Palpitoad, Seismitoad: Venom Drench
Sewaddle, Swadloon, Leavanny: Grassy Terrain
Cottonee, Whimsicott: Misty Terrain
Petilil, Lilligant: Encore
Basculin: Head Smash
Darumaka, Darmanitan: Extrasensory
Scraggy, Scrafty: Power-Up Punch, Acid Spray
Yamask, Cofagrigus: Crafty Shield
Trubbish, Garbodor: Autotomize
Ducklett, Swanna: Aqua Jet
Deerling, Sawsbuck: Headbutt
Joltik, Galvantula: Lunge
Shelmet, Accelgor: Toxic Spikes
Bouffalant: Cotton Guard
Deino, Zweilous, Hydreigon: Belch
Chespin, Quilladin, Chesnaught: Power-Up Punch
Fennekin, Braixen, Delphox: Psychic Terrain
Froakie, Frogadier, Greninja: Power-Up Punch
Flabebe, Floette, Florges: Tearful Look
Skiddo, Gogoat: Grassy Terrain
Spritzee, Aromatisse: Nasty Plot
Swirlix, Slurpuff: Sticky Web
Inkay, Malamar: Guard Swap
Hawlucha: Feint
Dedenne: Tearful Look
Phantump, Trevenant: Power-Up Punch
Pumpkaboo, Gourgeist: Curse
Litten, Torracat, Incineroar: Power Trip
Yungoos, Gumshoos: Fire Fang, Ice Fang, Thunder Fang
Cutiefly, Ribombee: Powder, Sticky Web
Wishiwashi: Whirlpool
Dewpider, Araquanid: Sticky Web
Sandygast, Palossand: Curse
Pyukumuku: Spite