Hi,
Would it be correct to assume that this is one of the AirPrint-compatible HP OfficeJet Pro 86xx e-All-In-One models listed in About AirPrint - Apple Support?
An AirPrint printer can be used without having to install additional drivers, provided that the printer and a macOS computer are connected to the same network (Wi-Fi router).
In case of similar difficulties with AirPrint, and if the setup is OK, a problem with the router not correctly discovering/registering/detecting one or more devices can be suspected. If so, one can try the following procedure (in the exact order):
Power off the Wi-Fi router, the printer, the Mac computer, and all other devices/computers. Wait two to three minutes. Power on the router. Wait two to three minutes. Power on the printer. Wait a minute or two. Power on the Mac computer. Finally, power on all other devices/computers.
Reset the printing system on your Mac to solve a problem – Apple Support (UK)
Add a printer to your printer list so you can use it on Mac – Apple Support (UK)
Use AirPrint to print from your iPhone, iPad, or iPod touch - Apple Support