The USB3 ports are connected to the motherboard, not to the new case.
So, look at the motherboard's USB slots for those slots with a blue "tongue" inside the socket, which indicates USB3. A "black" tongue will indicate USB1 or USB2.
Some motherboards have USB3 "sockets" directly on the motherboard. Use a cable to connect from those sockets to the USB ports on the front-panel of the new case.