Anything wireless might be considered to be insecure due to the information being broadcast, which is presumably why there is a requirement that you are connected with an ethernet cable.
A wireless router would replace the ethernet router.
Phoneline > router > PC or other device.
So it sounds as though wireless is not an option which means you have to find a way to move the computer closer to the router or otherwise find an acceptable path for the cable to link the PC to the router.
You would replace the route with another one. If your current one, doesn't have the option for Wifi, usually all routers would support both wired and wireless access.
But if your current router is either old or cheap and doesn't support wireless access you just replace it with a new model, so no need for two routers.
Problem is wireless connection is less stable and less reliable, espacially when its across the house, so if you already got a wired connection, i would stick with this. Unless you trip over the cables multiple times a day.
You can still replace the router to have Wifi access with all your other devices, like Phone/Tablet/Laptop/... and still have your main PC connected via cable.
Is this the second tie you asked this question? I might as well post the same answer here.
As I understand it, you have a router in another part of the house, you want to connect to this router by ethernet. Is that correct? If yes then you only have two options, one run a physical cable through the house, two use a tool such as a PowerLine adapter. I don't think you can get a new conenction to the internet by connecting another router to the cable coax connection in your room although I am not familiar with cable as I have only used DSL.
If they demand a wired connection you have to use LAN cable. They will have their security reasons to demand that.
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2Opinion
If you are on wi-fi you are not hard wired... Ethernet (cat6 cable) can run 328 feet and still work fine if you don’t mind it running on your floor across the house... Aside from that you’d have to know how to run wires through your walls which isn’t rocket surgery, but is a pain in the butt climbing in an attic and dropping lines and pulling wires...
If you use a wifi connection then it is not hardwired. Signals can be picked up by otheres nearby. There are ways to connect by Ethernet and put the cable through the ceiling or walls so it does not get in the way.
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