Mac OS X Version 10.6.8
First, please edit your post to reflect the question (Setting up HP 4520, or some such) rather than the version of macOS you have.

HP has downloadable drivers for your printer here. With HP printers just Google the make and model of the printer along with "driver" or "download" to find what you need.

There is a problem though as the earliest macOS version supported is 10.8. You might be able to hack the installer to run and install on your version of macOS but I would bet that you still wouldn't be able to print.

You may be out of luck with this printer and your current version of macOS.