Adding old printer to new iMac

Locate the printers IP address and add it using the IP Address. Apple explains how in:

Add a printer to your printer list so you can use it on Mac - Apple Support

Look in the section titled "Add a network printer by specifying its IP address".

If you need a printer driver, you could perhaps check whether the HP 5.1.1 Printer Software Update package download from Apple would work (despite the System Requirements limitation). This would be experimental. It may or may not open/install/work. Look for something like the HP LaserJet P2055 version 19.13 driver listed in the referenced article Printer and scanner drivers for Mac - Apple Support.

As always, make sure that you have backup copies of all important files before testing anything. Software conflicts cannot be ruled out.

It may be a good idea to reset the printing system before a test. See the following article:

Reset the printing system on your Mac to solve a problem – Apple Support (UK)

You're welcome! Glad to hear that printing is working.

You mentioned an HP website. Or did you mean the above HP 5.1.1 link (download from Apple)? Just curious, since the latest driver on the HP support page for this printer appears to be for macOS 10.12 Sierra (https://support.hp.com/us-en/drivers/selfservice/swdetails/hp-laserjet-p2055-printer-series/3662052/model/3662058/swItemId/lj-65921-2).