@dj_paige is correct. There won't be any free upgrade. You will have to purchase LR Classic CC subscription.
If you still have LR4, you can try installing it on the Mac and using that if you want to save money, but I would definitely upgrade and IDK if LR4 will work on your new Mac.
FYI, after you install LR Classic CC, and you try to open the old catalog file, it will prompt you that it will need to convert the catalog to a new version. It creates a new version of the file and doesn't touch the old catalog version. All of the metadata will be readable (hopefully) in the new version of Lightroom, but the layout is very different from back then. If there's an issue with converting your ancient catalog file, LR Classic will tell you.
Also FYI, if you are looking to save space on your hard drive, note that there will now be two catalog files instead of one (the original and the converted file). Also, the Mac will start generating new preview files. So you can delete the old ones.
If you are trying to use the old LR4 disk to install LR4 onto your Mac via a USB disk drive, just open the disk and run the installer. Don't bother copying the disk over to your Mac. That probably won't work.
Can/should I reinstall Lightroom 4 on my new MAC from the original disc?
Should I download a version of 4?
Lightroom 4 (the 2012 version with the catalog) cannot be installed on modern Macs running Monterey, Big Sur or Catalina.
Modern Mac operating systems (Monterey etc) only support 64 bit software. Lightroom 4 (2012) includes 32 bit components, including the installer. Monterey cannot read or run older 32 bit code. Hence LR4 will not even install.
Some people stick with the old LR software and run LR4 from an external hard drive running Mojave or earlier. That may be an option if you know what you're doing.
Should I upgrade to a newer version and if so will this new version recognize all of my changes and catologing of my files?
You'll have to subscribe to a Cloud plan in order to run the current version of LR Classic on your new Mac.
Yes, you can open your old LR4 catalog with the new version.