You have an old printer which isn't compatible with AirPrint nor does HP supply an app for it. What you are trying to do may not be possible. You could try Print N Share but it is not free and I don't know if it would work.
SparkyJack - You can get adaptors but I have had an iPad for several years now and haven't missed a USB port at all. It syncs with my pc effortlessly. The same is true of my iPhone. I had a Samsung Android phone before and that was a real effort to sync.
Sorry for thread stray.
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