So if we get new moves at the Move Tutors in Ultra Sun/Ultra Moon, these are the most likely candidates:

>Aurora Veil (オーロラベール: Aurora Veil)
>Burn Up (もえつきる: To Burn Out)
>Gear Up (アシストギア: Assist Gear)
>High Horsepower (10まんばりき: 100,000 Horsepower)
>Laser Focus (とぎすます: Hone/Sharpen)
>Leafage (このは: Foliage)
>Liquidation (アクアブレイク: Aqua Break)
>Lunge (とびかかる: Jump at/Lunge)
>Power Trip (つけあがる: Audacity/To be Audacious)
>Psychic Fangs (サイコファング: Psycho Fang/Psychic Fang)
>Psychic Terrain (サイコフィールド: Psycho Feild/Psychic Field)
>Speed Swap (スピードスワップ: Speed Swap)
>Spotlight (スポットライト: Spotlight)
>Stomping Tantrum (じだんだ: Stomping Tantrum)
>Tearful Look (なみだめ: Teary Eyes)
>Throat Chop (じごくづき: Hell Thrust)

These are the moves introduced in Generation VII that aren't (currently) exclusive to a Pokemon family, aren't available via TM, and aren't a Z-Move.

Any hopes?