If you remove the bare drive from inside the old enclosure and install it into the new enclosure (assuming it's the correct type: i.e., SATA vs IDE) then the drive should run over the USB 3.0 connection. How much of a speed gain you'll get depends on the speed of the drive itself. No hard drive actually runs at full USB 3.0 speed, but you'll almost certainly see an improvement over USB 2.0 speeds.