Yes, it's recommended to uninstall all the other Norton versions before installing a new one, because it might create conflicts. In most of the cases:
The installer will refuse to continue until the old product is not removed.
Windows will run slow due to resource consumption. Norton is known to consume system resources, and if you install two similar products, then the performance will degrade slowly.
Note: Use the Norton Uninstall Tool to get rid of the current version installed on your computer.