Your HP printer doesn't support AirPrint - and your iPad doesn't support printing via a wired USB connection.
Apple AirPrint is a driverless connection protocol. A high proportion of modern printers intended for Home, SoHo and Business environments now support AirPrint.
About AirPrint - Apple Support
As your printer is not compatible with AirPrint, you might consider connecting the printer to a PC or Mac computer - and install a “helper application” that allows the computer to emulate AirPrint capabilities. A further alternative is to consider installing a dedicated Print Server Appliance on your network - and connect your printer to this. One example is the Lantronix xPrintServer.
The remaining and potentially more cost effective solution is to simply replace your printer with one that is AirPrint capable.
See:
Apple AirPrint is a driverless connection protocol. A high proportion of modern printers intended for Home, SoHo and Business environments now support AirPrint:
About AirPrint - Apple Support