When you regain control of Lara, turn around and run to the left. Jump on the stone ledge and then jump to the ledge in the corner.

The red colour indicates from where you need to jump. This corner is the closest to the ledge you are heading to. The green colour shows the corner you need to land.

The yellow dot shows where you landed. Go around to the left and jump over the gap. Then go to the right around the corner.

Go to the end of the platform...

... but do not go up the stairs. Instead, go to the left and jump to grab the opposite ledge. On grabbing the ledge (even from the side), the cut scene plays.

If Lara lands on the ledge, you just need to hang. If you cannot reach this ledge at all, go up the stairs and drop from the part where there are no railings (opposite the entrance of the Monastery).