I upgraded to Big Sur 11.3 and the Samsung ML-1865 printer don't works anymore

The Samsung ML-1865W and ML-1865WK devices are supported by Apple's built-in AirPrint when networked. You will not need any software or drivers from any other source, including HP to support this printer. The AirPrint listing has them shown as HP-branded devices, not Samsung.

With the ML-1865 networked and powered on, visit System Preferences > Printers & Scanners panel, and right-click on the device entry in the Printers listing. Select Reset printing system… from the secondary menu. This will briefly remove the device from the Printers listing, open a Bonjour panel indicating that it discovered the ML-1865 on the network, and then you can re-add the device by selecting AirPrint as the driver. This is how my Samsung ML-2955ND is supported.

Yes, that was one of the print server models I had in mind, but I understand that you do not want to spend money on something that may not work in the end. You could perhaps find a used print server via an online auction site. A network connection (see also Add a network printer by its IP address in Add a printer on Mac - Apple Support) would potentially avoid some problems. One may have to try/use/select drivers for other printer models with the UPD.

Have you tried adding the driver through the built-in open source driver support?

Make sure the printer is connected via USB, and is the only printer connected.

Apple menu -> System Preferences -> Printers and Scanners.

When you go to add a printer using the + symbol, hold the Option key on the keyboard.

This will force it to find the open source driver of the attached printer.

Unfortunately HP's website stops support for this printer with Mojave. Which means if the open source drivers don't support it, they haven't written a 64 bit version of the driver. 10.15 and 11.0 are 64 bit, and require 64 bit drivers for all printers.

Unlikely I'll have news. I'm just a volunteer here. I would contact HP support and let them know the importance of being up to date on drivers. They are the ones holding you up on your Mac's security. If they can recommend a printer that takes the same Toner/ink as the Samsung that is Big Sur compatible with its drivers, that probably would be the next step.

Hi,

Still theoretical, but if nothing else works, could it possibly be worth testing a small external print server with the ML-1865 and the Samsung Universal Print Driver V3.93.01? There are USB print server models for Ethernet or Wi-Fi from a number of manufacturers.

The general installation information in the HP article https://support.hp.com/us-en/document/c06520117 in fine shows a network connection.

And AirPrint will never support this device if it is USB-connected. Does your particular ML-1865 allow you to network it, either with an Ethernet cable, or wireless configuration?