Is AirPrint installed on an HP Color Laser Jet Pro MFP M477fdw?

You need to connect that printer to the same Wifi Network where your iPhone is connected to, but I'm not able to find that HP model among this list: About AirPrint - Apple Support

To be sure (since the list has been updated on April 2020) you can contact HP and ask them.

Regards

Giulio

Your MFD is not listed as Air Print capable on https://support.hp.com/au-en/document/c03839843