I am trying to install an older version of a Hewlett-Packard LaserJet P3015 to my Mac computer

What OS are you using?

If there is no automatic option when attempting to add the printer, then select the driver drop down list to see if there is an option for "GutenPrint" or "CUPS" driver, but if those options are not available, then select the "Generic PostScript Printer" driver or "Generic PCL Printer" driver.

If none of these options are listed, then you may need to install the CUPS driver using the CUPS web interface using a web browser. You will first need to enable the CUPS web interface using the Terminal app and the following command (press the "Return" key at the end of the line to execute the command):

cupsctl  WebInterface=yes

Then launch a web browser and enter the following URL into the browser's address bar:

http://localhost:631/admin

When you click the "Add Printer" button you will be prompted to enter your macOS admin user name & password. It can sometimes be a little tricky adding some printers as you will need to know their DNS Name, IP Address, or possibly USB address/port number if the printer is not automatically seen.

Hello,

To begin with, it may be a good idea to reset the printing system. Does the operating system offer a suitable driver to use?

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

Add a printer on Mac - Apple Support

If necessary, check whether the Dec 11, 2020 HP Printer Drivers v5.1 for macOS (https://support.apple.com/kb/DL1888?viewlocale=en_US&locale=en_US) package can be used instead. Look for something like the HP LaserJet 3015 or HP LaserJet P3010 Series version 19.13 driver in the referenced Printer and scanner drivers for Mac - Apple Support article.

Connect that PCL and Postscript Network printer to your Router with an Ethernet cable, and when you go to Add-A-Printer, the driver should becomes available. If not, use generic Postscript driver.

Using Ethernet, there is no issue with authentication and network passwords, and every computer on your network can print to it easily.