The stairs located north of site of grace will lead to the point of activation for The Radahn's Great Rune. To get the Godslayer's Greatsword you must turn south, then go down the stairs. Be on the lookout for 2 Redmane soldiers near the bottom, one hidden behind the corner.
What is next is what follows is a FromSoft classic that is as famous as Miyazaki's love of poison swamps. It's the old "drop from edge to ledge on your way to the bottom of the great pit" set piece. (See also The Great Hollow, Majula, and the Hunter's Workshop). The path is fairly straightforward: your first goal is the cage elevator, with an Redmane soldier guarding it located slightly to the left your starting point. The strut that's cracked in your path is likely to break under your weight, but it's scripted so you won't suffer any damage from falling, and this is the path you need to go down.
Go up the elevator and follow the staircase towards the top of the hill. Make a detour to the ladder and enter the door at the top. It's an escape route back to the one and only place of grace. There's a monk wearing a blackflame further down the hallway, with plenty of poise and threatening incantations but he should not pose the risk of being a danger.
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