It's not necessary to uninstall a previous version of Final Draft, but it's also not necessary for the older version to be installed before you install the newer version. Leaving an older version on your computer will not interfere in any way with the operation of the newer version, but will take up some hard drive space. Basically, it's up to you.
If you do want to uninstall the older version, make sure to uninstall BEFORE you install the newer version. If you don't, it's possible for the uninstall process to remove components installed by the newer version and this can leave you with an incomplete installation of the newer program.
IMPORTANT: Before you uninstall an older version, be sure to deactivate it.
If you've started a script and are in production, you should complete the project in the version in which it was created. We don't recommend switching software of any kind in the middle of a job for any reason.