An NPC named Parcy at Riverside Stable will give you the “The Royal Guard’s Gear” side quest relatively early on in The Legend of Zelda: Breath of the Wild (depending on when you happen across Riverside Stable). You won’t be able to finish it until you venture into Hyrule Castle, though.
The entirety of this side quest is just finding and bringing back a Royal Guard item — and they’re all weapons because there is no Royal Guard armor. The problem with the weapons in this series is their shockingly low durability. This just means that if you want one to survive to show to Parcy, you’ll either have to save it without breaking it or leave Hyrule Castle early.
Where to find The Royal Guard’s Gear side quest
Where to find Royal Guard’s series weapons
There are five items in the Royal Guard series: the Royal Guard’s claymore, spear, sword, shield and bow. The short answer here is that you can find them in Hyrule Castle and then you can just return to Parcy as soon as you pick up a weapon with the words “Royal Guard’s” in the name. There are plenty to pick up as you wander through the castle, so you’re bound to come across a few.
If you’re more interested in just getting it done, there’s one right by an entrance that you can get without a lot of hassle. Head to the north side of Hyrule Castle and look for the tunnel that takes you back to Saas Ko’sah shrine. This is the way we recommended getting into Hyrule Castle. Instead of heading back into the castle along the tunnel — or, better yet, after you head down the tunnel and unlock the shrine — look for a doorway to the right (east) of the tunnel.
Just inside, you’ll find a large metal portcullis you can prop open with cryonis. Go around the corner and look into the cell on your left. Shoot the eye to clear away the malice and open the cell door. You’ll find a Royal Guard’s claymore just laying on the ground.
Backtrack out of the castle and travel back to Rota Ooh shrine and Riverside Stable. When you show up, Parcy will ask to see the sword (or whatever you happen to have picked up), then reward you with a gold rupee.