how do I get HP photosmart 7520 working with my NEW Imac?

Hi,

An HP Photosmart 7520 e-All-in-One Printer is listed in About AirPrint - Apple Support as a printer supporting the driverless AirPrint technology. An AirPrint-enabled model is compatible with macOS, and does not require the installation of drivers if the printer and the computer are connected to the same network (Wi-Fi router).

Add a printer on Mac - Apple Support

Have you asked HP about this.

click here,

https://support.hp.com/us-en/drivers/selfservice/hp-photosmart-7520-e-all-in-one-printer-series/5199461/model/5199462

make sure the operating system selector is set to macOS 11

click on the plus button to reveal the download.

Or reset the printing system on your mac.

Reset the Mac printing system to solve a problem - Apple Support