Our cat has started using the carpet as a stratching post at every hall door. She used to tap on the door 2 get attention. Now the fibres are being plucked out of the carpet. any solutions?

Clear plastic carpet runners cut to fit snugly around the door frames.
If you nip it in the bud early you may not have to leave them down very long.

Or a light dusting of pepper dust on that spot will deter the cat

Or a nicer scratchy surface. My Impossible Princess keeps trying to get under my hearth rug. I don't know what is so exciting about it.

Some questions -
Does your cat have a scratching post?
Is she an indoor cat?