Once you start actively looking to expand your Pokédex in Pokémon Legends: Arceus through evolving the various Pokémon you have encountered, you will need to begin collecting evolution items to complete Research Tasks.
Just like in most Pokémon games, Evolution Stones make up a decent number of item-related evolutions, and all of them make a return in Legends: Arceus.
Specifically for the Sun Stone, players will only really need one to evolve their Petilil into Hisuian Lilligant. However, you will need to do that a total of 10 times if you want to complete the Pokédex entry for the Flowering Pokémon.
Players can grab multiple Sun Stones at Ginter’s Specials in Jubilife Village for 5,000 PokéDollars once it becomes available, but early on you might want to save up your Merit Points from returning lost satchels to get one at the Trading Post instead. They are available in the Trading Post’s Item Exchange, along with multiple other evolution items, for 1,000 MP.
You can also grab one by completing the A Home Under the Eaves request, digging them up while riding Ursaluna once it’s unlocked after the seventh main story mission, or in space-time distortions as a rare item drop.