Prokaryotes, like most living organisms, need movement to locate food and to survive. if a prokaryote needed to move to a new food source, which structure would it use for locomotion?

A Prokaryote typically will use flagella to move where it needs to go. The flagella spin and provides propulsion through whatever liquid the Prokaryote is currently residing in. Much like a boat's propeller. That is the primary method of locomotion for Prokaryotes.