My female cat is 15 years old and I need to introduce her into my sisters house who has a neutred Tom cat about half her age.My cat is very inactive having arthritis in her hind quarters and is a very loving docile creature - my sisters cat is very fit and healthy and again has a nice nature but not as docile. Can you help.

I don't consider a neutered cat to be a "tom." That makes a world of difference for a male cat.

That's going to be a pretty drastic change for a 15 year old cat, so it's like dealing with two issues at once. One, that she's going to a new home, and two, that there's another cat there. Plus, it's your sister and not you (though she may know your sister well, I don't know), and it's already the other cat's territory. A bit more difficult than bringing home a new young cat from the shelter or something, but people do bring home older cats that have been in another home and make it work. (Even really scared abused cats can eventually adapt.)

I don't know if you're going to your sister's as well. It'll be easier if you are. If not, I would gather up some old junk of yours, especially things with your smell, like maybe some old (preferably unwashed) clothes or blanket or something like that. The familiar smells will help. In fact, if you're moving there too, it might help to put some of those things around the house.

Is there a place that you can make "her room"? That doesn't have to be permanent, but it would be a safe haven for her to use. You could put all her stuff in the same place - I would have a separate litter box as well as the food bowls. And feed them separately. And you can put some of your smelly things in there, and her toys, etc. And start her in that room alone. If you're there, spend some time in there with her. Your own bedroom would be a good place. Although you may also need to take her with you as you move about the place. She's going to be a better judge of that than you. Different cats will react differently.

Being older and having to leave her home is going to make it difficult on her and she'll really need some time to adjust. So not having to deal with other cats, people and objects may help her. You can slowly introduce her to other things. If she has her own space, I would introduce her to the other cat somewhere else in the house. If anyone has a cage, you can put one in the cage and let them sniff and hiss and whatever they want to do with the cage blocking their way. They'll end up on two sides of a door meowing at each other anyway. (Be prepared for it.)

Under normal circumstances, when I introduce a new cat, I let the cats do what they want. The new one tends to find a hiding place, like under my bed. I let them stay there and come out of their own accord when they're ready to do so. In the meantime, I put a litter box wherever they've chosen to hide out, plus food bowls. If that's my bedroom, I generally put the new cat in the bathroom at night cause my cats always sleep with me and the already established cats would have a cow if they couldn't do so. So at night is like the exception when I decide where the new cat is going to be shut up. I also shut up the new cat while I'm gone, but that can be the place the cat has chosen. Eventually they come out. I keep the cats separated at night and when I'm gone until I feel comfortable that they won't kill each other while I'm not there.

I also let the cats deal with each other on their own terms. They will decide who is boss and I don't interfere. Sometimes that process takes a while. I don't worry about hissing and meowing and even scratching and whatnot, unless it looks like one might seriously get a hurt. (Really, I don't think I've ever stopped a situation like that -- not sure it ever got to the point where one would seriously get hurt. Though I did once have a situation where I had to keep quite an eye out.)

The only real difference here is that the "new" cat is the older one, coming from another home. I'm kind of thinking from the point of view like when I had an older cat who was very docile and complacent, and introduced a new young, rather wild cat into the picture. That really freaked out the older one. (He also had diabetes and that made his blood sugar freak, so I was trying to keep him as calm as possible.) And what I've just described is what I would have done if it had been him. If he had not died of cancer, he would have been moved at about that age into my new house.

That's just some of my ideas - there are others.

And accept the fact that the two cats may never become friends. The important goal is making sure they're at least tolerating each other. Given her age, I doubt they'll start playing together. But it's a nice bonus if they at least form a relationship of some sort. My two cats don't ever sleep together (except on two sides of the same bed), or groom each other much or anything. But they horse around together, sometimes a little more seriously than others.

Someone else just posted about traveling with a cat and I recommended Rescue Remedy. That may come in handy for this situation as well, so here's the same link:
Rescue Remedy Flower Essences for Pets | Natural Pet Health