Connect my printer to my laptop using a cable

[Pollywog999]

I initially put out a call for help with getting my HP  LaserJet MFP M139 M142  printer (which also seems to self-identify as LaserJet MFP M139w on some of the printer test pages) to print from my MacBook Air.

When I originally set up my printer, it was attached to my 11-year-old iMac, and the machine printed pages, photocopied, and scanned using a cable between the printer and iMac.

Weeks later, the error light began blinking, and  the printer stopped working, aside from photocopying. Someone suggested that there was a conflict with the router which was a foot or so from the printer. I put a cookie sheet between the router and printer, and was able to print and scan. Then the printer stopped printing and scanning. "Printer Not Found".

The recently-acquired MacBook Air was wireless, but I could not get a connection to the printer. Used the cable, and still no connection.

I want a cable solution. I do not want a wireless connection. I plan on printing from my work desk, with the laptop and printer sitting side-by-side.

BeemerBiker got right back to me after I posted my initial call for help. We had some back-and-forth exchanges, as I tried to nail down what I understood, and what I was not understanding. The main problem was that I am not tech-savvy (75-years old, which might be an issue, as well), and drive a Macintosh (OS 15.6.1). I have used Windows machines on occasion, but not in the last 20 years. Never owned one.

During the source of reading some of the material I acquired through BeemerBiker, I found references to using an ethernet cable for connectivity. What I have right now is the standard printer cable with a square-ish male plug for the back of the printer, and a USB 3.0 end to connect with either of my two Macs.

Is there a fix for my problem that allows me to use my original cable, as described, or do I need to upgrade my cable?

And is there such a thing as a cable with ethernet on one end and the printer plug on the other, or would accept the USB 3.0 end of my cable and provide the ethernet connector at the end that could go into my MacBook Air (which does have an attachment with a bunch of openings for about every kind of plug presently in use, including ethernet)?

And if there is a cable solution, am I still going to have to subscribe to HP: Print and Support, with a free trial at the minimum, and the possibility I will need it at intervals when my "Printer Not Found" becomes part of my lifestyle.