Unlike most Pokémon games, evolution in Pokémon Legends: Arceus isn’t automatic. You need to meet certain requirements and evolve them manually. Ursaring is much the same.
To evolve Ursaring into Ursaluna, a Normal/Ground Pokémon unique to Hisui, you need to use an item called a Peat Block on it during a full moon. You can find Peat Blocks by digging in Crimson Mirelands using Ursaluna as your ride. They’re a little uncommon, but keep using your Treasure Detector and have Ursaluna dig when you’ve detected something valuable nearby.
If it’s not the full moon yet, return to camp and sleep until night again and again until you get one. You don't have to check the sky to know—just open your satchel and see if you can use the Peat Block. If you can, then it's a full moon.
Unfortunately, Ursaluna is not the best Pokémon for battles. Its typing makes it vulnerable to four kinds of attacks: Water, Grass, Ice, and Fighting. A Fire type in your team can cover most of Ursaluna’s vulnerabilities. It's strong against Poison and Rock types, which are both uncommon in the game.
On the upside: Ursaluna has an incredibly high HP and Atk stat, which your grit items should be going to first.
For more help with Pokémon Legends: Arceus, we at Pro Game Guides have you covered.