It should be possible to add a new cordless (as they used to be called) handset into your system, though it may not be as simple as you might like it to be.Frankly, given how cheap these things are you might be better off just starting again from scratch and getting a matched set of handsets and base-station/answering machine. The advantage of this is that the handets come pre-connected so there should be no complicated pairing to go through.Here's a BT package, you might consider, though there are others to choose from.BT XD56 Quad Cordless Phones with Answering Machine and Nuisance Call Blocker https://amzn.eu/d/5TlPlbjDo bear in mind though that as someone else has said, all landline phones will soon be connected through a broadband router which may or may not be in a convenient place to have your phone's base station. Help and advice should be available from your service provider - in your case BT.
Bruce Hammal ● 7d