If you have a perpetual license, it will run for longer than a year, it just stays at the version after the year of support is up. If you miss the 1 year sign up, and you want to upgrade it will require you to buy a new licenses at whatever MSRP is at that time. And now you’ll have two licenses; your original one stuck at the version forever and the new one which will have support for 1 year unless you let that lapse, and so on and so forth. If you pay the $299 support fee, then you can grab whatever is released when released.
But that being said, yes ,De-authorize, install version on new Mac, and authorize there.
Michael