NO.Do I need a new gateway
(uplink.wan.port)existing.router(one.lan.port)----(any.port)new.switch(3 more ports)
NO.
you can use a HUB or a SWITCH - - the latter is a better choice. neither use an IP address.
wiring is like
If you need to add WiFi, then use the same wiring as show, but get a WiFi router. Come back here andCode:(uplink.wan.port)existing.router(one.lan.port)----(any.port)new.switch(3 more ports)
we will help you config that choice.