If you remove and repour just the center slab, you’re going to change the pressure against the ground which is likely to cause some shifting among all the surrounding tiles. You’re definitely going to find someone willing to replace just the center tile, but if you do that you’ll almost certainly be in a position in a couple years where you’re looking to replace the whole thing.

I’d save up to remove it all, and think creatively about what an entirely new patio could look like. You don’t have to replace it on its current footprint, but I can’t see enough of your space in this picture to give you any layout recommendations.