Z-moves were one of the main battle gimmicks added in Pokémon Sun and Moon to try and signify the band between you and your Pokémon. Both you and your Pokémon’s wishes would combine to create a powerful attack to decimate your opponent. While Z-moves returned in Pokémon Ultra Sun and Ultra Moon, they did not make an appearance in Pokémon Sword and Shield. That being said, are Z-moves in Pokémon Legends: Arceus.
Unfortunately for any big fans of Pokémon Sun and Moon, Z-moves are not in Pokémon Legends: Arceus. Instead, the main focus in this game is traversing the land with your trainer and catching Pokémon various ways. When it is time to battle, the moves you have are pretty standard attacks that you have seen in past Pokémon games.
With Z-moves being an exclusive battle element of the games that take place in the Alolan region, we would be surprised if they returned any time soon. Maybe if the games were to get some kind of remaster or port in the future it is possible, but we would be highly surprised to see them make a return in any other game. Not to say that is impossible, just do not get your hopes up.