Please check if you are going to reinstall in the same operating system or not.
If the operating systems are the same, that is to say, from Win to Win or from Mac to Mac, then you can directly download the software into your new computer and then login with your ID.
If the operating systems are not the same, please note that we don’t support to switch the plan between different platforms. You’ll then need to purchase a new license to work in the new system.