looking for hp LaserJet 1600 driver for Mac/Catalina OS

Open >System Preferences>Software Update (Command R will reload and do a fresh check)

Update: HP Printer Software 5.1 should now be becoming available through Software Update to fix this issue.

(2220 UTC 23 October 2020)

or Apple direct download:

https://support.apple.com/kb/dl1888?locale=en_US

If you have continued issue:

The solution is to download this package which will update drivers AND THE CERTIFICATE:

ftp.hp.com/pub/softlib/software12/HP_Quick_Start/osx/Installations/Essentials/hp-printer-essentials-S-5_14_8_4.pkg 


download link above at the ftp address

If you still have an issue, and listed as AirPrint printer, delete the existing printer in

> System Preferences> Printers & Scanners, and add it again, select AirPrint.

Connect an AirPrint printer to a Wi-Fi network - Apple Support.

https://support.apple.com/en-us/HT201900

about AirPrint

https://support.apple.com/en-us/HT201311

you can also try reset print system if necessary:

If you can't print from your Mac or iOS device - Apple Support

https://support.apple.com/en-us/HT203343

If you are still at a loss: https://123.hp.com/us/en/