Yes, of course, you can move your license to new system any time when required. It is possible unlimited times. The only requirement is that the
license should be used on 1 computer at any given time.
The best way to move the license (together with all settings, statistics, logs): please use Configuration -> Update -> Backup configuration to save all settings, statistics, registration and activation details to a single file.
After installation on the new system, this file can be loaded back by Configuration -> Update -> Restore configuration and then the software will be registered, activated immediately. It may be good if you prefer to keep existing statistics/logs for drives you want to use after re-install.
If you prefer a clean, fresh re-installation, generally there should be no problem: the activation server allows reinstalling (or moving to new system) any time. Problem could happen only if this happens too many times (or too frequently), then the license may be blocked.
So if you prefer a clean reinstallation, you can proceed the activation exactly as you did last time by using the original 15 digit registration code.