|What kind of switch are you using right now? |
If it's an L2 managed switch capable of VLAN tagging then it's as simple as creating a separate VLAN for the new external connection and it's associated clients. Add as many ports as needed to the VLAN, connect the router's LAN port and the clients to the other ports in that new VLAN and it will work.
If however you don't have a managed, VLAN capable switch, I would suggest you buy an 8 port switch (or one with more ports if you figure you'll be adding more clients in the future) plug the new router's LAN port into that switch along with the clients that will be segrated with that router.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.