Does your printer support AirPrint? No, it doesn’t - and this is your problem.
If you look, you may be able to find an HP Print App for this printer in the Apple App Store.
As your printer doesn’t support AirPrint, if you cannot find a corresponding HP Printer App, then you have to connect your printer to either a PC/Mac (and install an AirPrint “helper” program where needed) - or a dedicated AirPrint Print Server appliance (e.g., Lantronix xPrintServer).
It may be cheaper to “retire” your old HP printer - and replace it with a modern printer. With limited exceptions, most “consumer grade” printers now support AirPrint.
I hope this information is helpful in explaining why you have a problem - and in providing multiple solutions from which to choose.