Which option correctly describes the orientation of an arrow pointing North after it undergoes a $225^{\circ }$ clockwise rotation ?

Let's break down the $225^{\circ }$ clockwise rotation starting from the North direction:
1. Rotating $180^{\circ }$ clockwise changes the direction from North to South.
2. Rotating an additional $45^{\circ }$ clockwise from South moves the orientation to South-West ($180^{\circ }+45^{\circ }=225^{\circ }$).

Thus, the final orientation is pointing South-West.