How the membrane potential generated by proton pumps is used to move K+ down its electrochemical gradient?

The hydrogen ions which were built up on the outside of the cell, forms a stored energy due to the proton pump moving a positive charge, in the form of H+ out of the cell. This creates a membrane potential in the cell where the inside of the cell is negative. This charge separation is a form of potential (stored) energy that can be harnessed for cellular work.