The headphones you bought previously (based upon your earlier post) aren't Bluetooth ones. They use an older technology, whereby FM signals are broadcast from the base transmitter unit to any suitable receiving device in the area. (i.e. your next door neighbour, using a set of headphones on the same frequency, could also listen to the sound from your TV). Bluetooth headphones use a form of encryption, whereby the sound from the transmitter unit can only be received using headphones that have been specifically paired with it. So your new Bluetooth headphones can't be paired with the older base unit because that transmitter isn't a Bluetooth one. (Although your existing base unit, and the headphones that came with it, use an older technology, it still has certain advantages in that the signal carries further and can be more reliable, which is why I was happy to recommend those headphones to you).
To get your new (Bluetooth) headphones to work with your (non-Bluetooth) TV, you'd need to replace the FM transmitter unit that you've been using with a Bluetooth one (which plugs into the same socket), such as this one:
https://tinyurl.com/4pmap3yt
(There are cheaper models available on Amazon but the reviews for most of them don't look good to me). Your existing base unit doesn't need to be charged (because it's powered by the main adapter) but that Bluetooth base unit requires charging via the supplied USB lead, giving up to 8 hours of listening time (which is more than some cheaper models do).