This page offers a guide on how to complete Request 41: An Elegant Tale in Pokémon Legends: ARCEUS (PLA).
You can pick this quest up from Asabei, who’s found on a cliffedge overlooking the farm and the southern gate. He’ll ask you to show him a Pokémon with “a tail that curls like a spring”.
Where to Find a Glameow in ARCEUS
The Pokémon in question is a - a small cat-like Pokémon with a springy tail. You can find around Veilstone Cape in Cobalt Coastlands. They’re a hostile Pokémon so if you want to catch one outside of battle you’ll need to be sneaky!