Extension phones are not your providers responsibility , assuming BT are your provider, (otherwise why post here ) this isn’t a BT issue (or an Openreach one either ) ….if it is a wired extension , it’s possible the phone itself is faulty or the extension socket or the wiring (cabling) to the extension socket is damaged/faulty .
If your purpose posting here is to try and get the extension phone working again , the first thing to try is a different phone ( a known working one ) in the extension socket to prove if it’s the phone or the wiring , if a known working phone has the same issues , then the wiring /socket are likely to be the issue , obviously if a different phone works, then the original phone is faulty.
If your extension phone is a cordless phone , obviously it can’t be wiring or an extension socket .
