What energy conversion takes place as an arrow is shot from a bow?
Potential Energy is converted to Kinetic energy.
By virtue of the string of the bow being stretched, the amount of energy that it took to stretch the string is stored in the string as long as the force keeping it stretched is intact. When the force is released, the stored potential energy is converted to Kinetic Energy, which is the energy of motion. The motion of the string launches the arrow by virtue of being in contact with the arrow.