The following models are listed in About AirPrint - Apple Support:
- HP Color LaserJet Pro MFP M479dw
- HP Color LaserJet Pro MFP M479fcdn
- HP Color LaserJet Pro MFP M479fcdw
- HP Color LaserJet Pro MFP M479fdn
- HP Color LaserJet Pro MFP M479fdw
- HP Color LaserJet Pro MFP M479fnw
Do you have one of these exact models? If so, the printer would be an AirPrint model, meaning that it can be used without additional drivers. This should be OK with macOS 10.14 Mojave, too. AirPrint works with wireless (Wi-Fi) or wired (Ethernet) network connections. You may want to run a test with the printer connected by Ethernet cable to one of the LAN ports of your Wi-Fi router.
Otherwise, if you for some reason want or need to install printer drivers, and HP Easy Start does not allow you to do this, you could perhaps try HP Easy Admin instead:
https://support.hp.com/us-en/document/c06164609
Alternatively, check whether this package from Apple contains something useful:
HP 5.1.1 Printer Software Update - Apple Support
If nothing else works, try a generic PCL or postscript printer driver in macOS:
https://support.hp.com/us-en/document/ish_4037000-4037075-16
Add a printer on Mac – Apple Support (UK)