She’ll get as much, possibly more, equipment from a private hospital than from an NHS one. I bought a sock putter-on, and a grabber, but my private hospital would have provided them if I had not. They also gave me a raised loo seat, crutches and a walking stick.
OP, find out if she can have anti-coagulant injections rather than compression socks, as they are a bugger to manage after a hip replacement.
I found a plastic bag on the front (passenger, obviously!) seat of the car useful for swivelling into place for the drive back from hospital, and for car journeys for a while after my op. And as a PP said, another for the bed.
Raised loo seat for sure, grabber (helping hand) with a magnet, sock putter-on. Ask if any or all of these will be provided before you buy them.
Wipes, and a long handled sponge (with a curved not straight handle) were useful early on.
Before she goes in, make sure that her toenails are short - it was weeks before I could cut mine easily and I hated asking for help with that.