The Royal Guard's Gear
Talk to Parcy to get this quest.
She wants to see something from the royal guard's series, which means any piece of equipment that begins with "Royal Guard's..."
Venture into Hyrule Castle to find something that matches that description and return to her. Equip it and show it to her to complete the quest.
Afterwards, she will be willing to buy similar pieces from you for ore.
Pieces from the royal guard's series include: