Provided you TV has Wi-Fi it should be able to connect to the router they send you. A lot depends on the type of house you have and how it is constructed. Can you get Wi-Fi on a tablet/phone/laptop in the place that the new router will be located? If you can then it will probably work.
Wi-Fi struggles to get through stone and brick, and some houses are internally walled with board that has a foil on the back, which will also stop Wi-Fi in its tracks.
If you currently connect your TV using a Ethernet cable to your router then you could use TP Link Powerline devices to keep this arrangment. The adapters plug into your mains sockets and send the data over your mains to wherver you need it.
Alternativly you could run a long ethernet cable from your routers new position to your TV.
Unfortunatly without trying it you won't really know.
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I remember the Internet starting!
Sky Full Fibre & Virgin Media XGS-PON, with automatic failover using DrayTek multi WAN router.
Sky Q, which is sadly missed when they decide to kill it off!
