The connection on the rear of the printer will be USB "B" which is a kinda square thing.
So you need a USB 3 to USB "B" cord. That said, the actual USB 3 connector looks the same as a regular USB 1 or 2 connector but cannot carry the extra speed of the USB3 link but can carry the data stream for the printer, so I would be worth trying your existing USB cable first.
There is a special USB 3 printer connector which has two connectors on it but I doubt this will fit your older printer
I'm a little embarassed to ask this, but: I'll be getting a Macbook Pro with (2) USB 3 ports and I want to connect an older HP OfficeJet 4500 printer to it. The printer documentation just identifies one USB port in back. I need a pretty long connection between them - what do I look for to buy?