If your spare Router is a Cable/DSL Router (i.e. *without* a built-in Modem) it can simply be plugged in via its ethernet WAN port to the existing cable and used as a "sub-router".
If it is an ADSL Modem/Router, it could be used as a basic Wireless Access Point / Network Switch. Disable its DHCP Server and connect one of its LAN ports to the existing cable, then connect the PC to another LAN port and the printer to it "wirelessly". In this scenario, it *WON'T* function as a router, only as a Network Switch, because its WAN port cannot be connected.