Head north from the survivor's camp, stopping by the locked passage shown on the screen. Since you already have the rope ascender, you can use it now, combining it with the rope arrow to unlock the passage.
Approach the elevator control mechanism and interact with it, bringing the entire construction down. Now catch interactive edges in front of you and climb up to a higher ledge.
Stay on a small ledge and bounce off the vertical wall so Lara can reach the ledge and then interactive walls shown on the screen. Quickly take the climbing axe from the inventory and use it to finish first part of climbing (reward: 100 XP).