If you would like to use your Parallels Desktop for Mac license on a new Mac, you should sign out of your account in Parallels Desktop on the old Mac.
Click on the Parallels Desktop menu, and select Account & License. In the activation window, click on your account email address and select Sign Out.
If your old Mac is unavailable anymore and you can't sign out, then upon activation on the new Mac you will see a warning that the license is already in use.
If you click on Activate on This Mac, the current copy will be successfully activated, and the license will automatically be deactivated on the old Mac.
Move virtual machine
Note: a virtual machine (VM) created on an Intel-based Mac cannot be started on a Mac computer with M1 chip. A new VM on a Mac with Apple M1 chip must be created (see KB 125375). However, you can transfer your data from the original VM as per KB 125344.
If you don't want to lose work progress and install your virtual machine from scratch on the new Mac, you can move your virtual machine to the new Mac as well:
1) Make sure the VM is shut down. Don't just close the virtual machine window with a red button at the top left - shut down it with its guest OS means(for Windows it will be Start button - Power button - Shut down) or click Action at the top Mac menu and select Shut down.
2) Locate the virtual machine on your Mac.
NOTE: in order to transfer a Boot Camp partition, see KB 113658
By default, virtual machine files are saved either to the
Parallels folder inside your user folder or at
/Users/Shared/Parallels. Another possible location is the Parallels folder inside the Documents folder.
Parallels Desktop virtual machines have a .pvm extension
3) Copy or move the .pvm file to the new Mac and double-click it there to start the virtual machine on the new Mac.