So when my Internet Security ends in three months time, what happens when I change to 360, do I have to uninstall security to install 360?
When you have the new product key for your new 360 product, you can enter your product key into your current Norton product. That will initiate the upgrade process to uninstall the old product and download and install the new product. From your current Norton product, click on Help > Enter Product Key at the bottom right.
Be sure you do this with only one or two days remaining on the old subscription so you do not lose any time from the old subscription.