Location: The Dalimil Inn
Petitioner: Sava, Apprentice Smith
Unlocked: Complete Follow the Crystals
Reward: 1 Goblin Coin, 10 Renown, 800 gil
In order to unlock this side quest you must first begin the main story quest Riddle of the Sands, which will take you to the Dalimil Inn, in the Velkroy Desert. Partway through Riddle of the Sands you'll have to complete a sub-quest, Follow the Crystals, and doing so will earn you a seal. This will unlock Carving Out a Niche.
The petitioner for this quest, Sava, is standing in L'ubor's smithy, a few steps away from the local Obelisk. Sava describes himself as the 'least' of L'ubor's apprentices, and needs to pass a test to remain in the smithy. Alas, L'ubor hasn't properly described the test, and he's not sure what to do. Accept the quest and you'll need to help him craft a carving knife to present to L'ubor.
Head down Dalimil's central street. There's a Flesher on your left, working in her stall, and if you check by the South Gate you'll find a Hunter. You need to speak to both NPCs, then head back to Sava for another conversation. He'll come up with an idea and take off.
Leave Dalimil and head north into the Velkroy Desert. Your destination is the huge, Fallen ruin in the middle of the desert, the one you passed to reach Dalimil in the first place. Sava is chatting with a merchant right by the southern entrance, and they'll conclude that Sava needs some limestone to create his knife.
Fast Travel back to the Dalimil Inn Obelisk and head south, through the South Gate, to the Doeznow Terraces. There's a spot near the South Gate where you can peer out at the springs of Fangsdrip, across the water, and here you'll find three samples of Spring Lime. Return again to L'ubor's smithy to hand over the limestone, and complete the quest.