Hi Jennyhannah and a big welcome to the Forum.
Yes, I'm afraid your aunt is right, at over four years old a hybrid hen will have used up all the egg cells she was born with in her ovaries, sort of the henopause I suppose, and will no longer lay. She may hang on in there as a pet for a while but she has done well to make it past the 4- year mark. Good hybrid layers live life in the fast lane, produce an egg nearly very day for 2-3 years, and after that egg production dries up and often, there are other problems such as prolapse or soft shells which are incurable due to age.
So, what to do? You would have to recognise that this bird has a limited life span left, and that at her age, rehoming will be a big upheaval for her. It would be lovely to give her some company, hens really don't like living in isolation as they're flocking birds, but if you get just one pullet, it will be hard to introduce her because a singleton is always bullied by older birds. Also, when the old hen finally pops her clogs you will again be left with a single, lonely bird. I would advise getting a pair of POL pullets, who will bond with each other, and introducing them carefully to the older bird, perhaps through a wire barrier at first, and preferably at a time when they all go into the new run together so its fresh territory to all of them. Then you'll have lots of lovely eggs for 2-3 years.
You will need a coop which is big enough for 3-4 birds, (the bug may well bite, and when you are down to two hens again, you may want to introduce another pair rather than a single one) and a foxproof run which gives a minimum of 2square metres of floor space per bird. For 3-4 birds, 8 sq metres is really the minimum as some space is taken up with feeder, drinker, dustbath etc. if they're overcrowded you'll risk problems of fighting! feather pecking etc! and the run will get filthy very fast. There are many coops on the market with small runs attached -beware, these coops may be adequate for roosting, but will not give the space that the birds need. Do you have any hen equipment already, or is your aunt maybe passing some on to you? Lots of advice on here about coops and runs, its important not to make expensive mistakes at this stage. We'll be looking forward to hearing more about your plans. There more information for new poultry keepers on the Poultrykeeper moan website, link at the bottom of this page, see http://poultrykeeper.com/ which you may find helpful.