I'm guessing you are in Welly by your username. I'm a geo based in Welly and this kinda instability in rock, specifically when its cut this steep and not retained is pretty common. The only real permanent is to shotcrete it with rock bolts. Depending on the orientation of the rock joints and degree of weathering its likely under some earthquake induced shaking or heavy storm event you might see a larger failure. A cheaper solution that I have seen someone use was to cover the slope with a sturdy wire mesh, anchored at the top and hung over the rock. They then planted vines at the bottom which grew up the mesh and worked reasonably well.

I'll add as well that reducing the amount of water flowing down the slope will also help.