I bought a 5 axis bench milling machine that came loaded with Mach3. I've been told that this Mach3 package is probably pirated so I am not eligible for support.
I plan to buy a Mach3 license but before I do, I need to ask the question...can I just enter the new license number on the existing package or do I need to uninstall and replace old with new package?

You will get a license file specific to you which is loaded into a folder though I can't remember which one. However you'd be well advised if you  can to load the recommended latest mach3 version.  I'm not sure what support you expect, Mach3 has not been updated for 10 years I think. However people here on the forum are very helpful. If you do load a new version be sure to copy across the latest config XML file from the old one as it customises M3 for the specific machine.

Oh and depending on what motion controller you have there will also be a plugin to customise the interface.  Is it parallel port, USB, or Ethernet? Finally, do download a copy of the Mach3 manual if you don't have one.