Whats a Bag Trap ?
The trap in this picture is not a P-trap. It is a bag trap. You will probably not be able to find a replacement any longer should you need one. Notice where the inlet to the trap is located. Its at the rear of the fixture, not the center of the basin. A standard P-trap thats available today won't fit. If the pedestal is open in its back side, the faucetry would have to be replaced and a modern pop-up assembly installed in the basin for the P-trap. If its not open in the back, and you have to replace the bag trap, then you may have to replace the sink in its entirety also.