If the remaining living part of the trunk is just a narrow strip up one side, then the tree will lack vigour. Because that narrow channel is all the tree has got to get water and nutrients up to the place where the fruit grow. Look at the size of it. Is it enough of a transportation route to achieve what you want? I had a tree that had a huge canker on it that reduced the living channel to very narrow strip, and the result was no vigour above. Fortunately I could cut the tree off below the canker and get a much wider channel for what regrew above it, and that tree has now restored its vigour, but it took a few years. You may not have any wider channel at a lower point. But you have to make sure you never cut the tree below the original graft, because then you'll be growing root-stock, not edible apple tree.

To get bigger, riper apples, you need to thin out the ones you have got out. It is good to do this even on a vigorous tree, but with your restricted it is even more necessary. But you'll only be getting a dozen or two.

Probably a lot less fuss just to plant a new one. You should never plant a new tree just where you took an old one out, so you must put it somewhere else. You can keep an eye on the old one for a few more years before deciding to take it completely down. Meanwhile your new one is maturing to fruiting condition, takes about 3 years.