Approach the right hand side of the pillar and step on the lower part of the floor. Hang from the edge and release to grab the handhold below. Lara will grab onto with one hand, so press the Interact button to help her. Traverse to the left as much as you can and release to grab the small handholds below.

Climb to the left until the vertical pole is behind Lara. Jump to grab it and slide to the bottom.