Pokémon Legends: Arceus is set to introduce Pokémon fans to a new batch of collectible creatures. Set in the Hisui region, an ancient version of Sinnoh, the region is home to all sorts of exclusive variants and evolutionary branches. Even the Starter Pokémon (Rowlet, Cyndaquil, and Oshawott) are rumored to have exclusive Hisuian evolutions. However, since this game takes place in times of old and none of these Pokémon have been seen before, many fans have concluded that these variants have all gone extinct.
If it's true that Hisuian Pokémon are no more, then that poses a problem for the anime. If they can't be found in the modern world, then Ash may have no way of interacting with them, so viewers won't get to see them either. However, the writers of the anime are no fools; they can find all sorts of workarounds to ensure that every aspect of the game that deserves to be advertised gets represented in the series.
There are a couple of possible ways for Hisuian Pokémon to appear in the anime. One possible method is through resurrection. As with Fossil Pokémon, perhaps it's possible to take the remains of one of an extinct species and use them to create a living, breathing specimen. It's hard to say whether this will be implemented as that method of finding old Pokémon seems like it should be exclusive to fossils, but the possibility certainly exists.
A more extravagant answer would be to travel back in time to ancient Hisui. If Ash and his friends were to travel back to when Sinnoh was still Hisui, they could see all the Hisuian forms they want. They might even bring one back with them to the present. The recent episodes of the anime have been dealing with Ash encountering Dialga and Palkia. Ash could somehow use Dialga's powers to travel back to the past.
Furthermore, there will be a four-part special featuring Arceus premiering in the near future. This special is apparently meant to coincide with the release of Pokémon Legends: Arceus in January. It will likely involve the Hisui region in some way, shape, or form. If this is true, then Ash will have a good chance to see some Hisuian Pokémon with his very own eyes.
However, if Hisuian Pokémon are introduced to the anime, there will have to be ways for them to at least make occasional appearances in future episodes. The concept of regional variants is still relatively new to Pokémon, so it's difficult to say how the anime will handle this new frontier. They could have Ash catch a Hisuian Pokémon or evolve a modern Pokémon into a Hisuian evolution. If Ash obtains a Hisuian Pokémon, then it can at least show up from time to time either in his party or at Prof. Oak's lab similar to other rare pokemon in the series.
Another solution is to discover that the Hisuian Pokémon never went extinct in the first place. It doesn't actually say anywhere that these Pokémon died out; so far, it's just a highly-plausible fan theory. Even if it were true, The Pokémon Company would still find workarounds to make it so that there's still room for change.
Of course, if Hisuian variants and evolutions ever were to show up in the modern Pokémon world, there would have to be an explanation as to where they've been. This could also be resolved the same way the anime has handled Fossil Pokémon. The Hisuian Pokémon could show up in places that are hidden away from the rest of the world where nobody would have found them. The anime does this all the time for Pokémon like Omanyte and Aerodactyl. Even the spinoff games like Pokémon Ranger and New Pokémon Snap don't strictly adhere to the rule that Fossil Pokémon have to come from fossils. Likewise, Hisuian Pokémon don't necessarily have to come from the ancient past.
Hisuian Pokémon will more than likely show up in the anime, it's only a question of how. Fortunately, there are all sorts of routes the anime can take to make this apparent impossibility a reality. Whether fans are formally introduced to these new Pokémon through the anime or the upcoming game, it will be a good opportunity to get to know them and fall in love with them.