You could stream your linux desktop to your TV using something like a chromecast stick.
I've never tried using chromecast, but that would offer the most portable and wireless option at relatively low cost. The only tricky bit might be getting it working - with any luck the following link has that covered:
https://www.linux.com/learn/how-stream-content-linux-system-chromecast
There are also screencasting programs like OBS Studio that will allow you to create a video stream of your desktop - but I think the streaming functionality requires a connection to some kind of web-based streaming service (e.g. twitch.tv, facebook live etc).
OBS should be available in the *buntu repos.
Offhand, I'm not sure whether OBS Studio allows you to create a localised stream on your local wifi network or not. So the downside to this approach is that your stream could be broadcast to anybody listening on the internet! :/
Another option (albeit a much more expensive option) might be to consider using something like wireless HDMI Extenders.
A quick duckduckgo yielded this:
https://www.startech.com/AV/Extenders/HDMI/
These things are quite expensive and aren't completely wireless, because they require two short HDMI cables (one to connect your TV to one of the extenders and the other to connect your laptop to the other extender). I think the extenders each have a power supply too - so there would also be a power cable required for each extender.
Although not a completely wireless solution - it at least means that you could use your TV as a second monitor on your Linux PC and you can have your PC further away than you could with a direct, cabled HDMI connection. (Typically HDMI cables are no longer than 2 or 3 metres - So with a cable your PC would have to be pretty close to the TV.)
By using a wireless HDMI extender, you could have your PC virtually anywhere in the house. It wouldn't be a particularly portable setup, but wireless HDMI extenders might be worth the expense if the setup will be a permanent thing - e.g. the PC in question is always going to be situated in exactly the same place.
So there are advantages and disadvantages to each option.
Personally, whenever I want to connect my Linux laptop to the TV in the living room, I just use a 2 metre long HDMI cable. Not at all wireless, but it's the simplest, cheapest and most direct solution for me!
After connecting my laptop to the TV, it's just a case of opening the KDE settings dialog and enabling the TV in the monitor settings page.
Also in the "audio hardware" settings tab of the audio settings page - change "full stereo duplex" to "HDMI output" to route all sound from your laptop to your TV.