First, you will need to download Solid Security Pro from the Member Panel (If you currently have the free version installed). This article will give detailed instructions on how to download from the Member Panel. Please note that the Pro features will not appear unless the Solid Security Pro plugin is installed.
This link will give steps on how to install a new plugin. Please keep in mind when adding the Solid Security Pro plugin, it will need to be in the .zip folder to be uploaded.
Then you can safely delete the free version while maintaining your settings (if you previously had the free version installed).
You can license the plugin by going to the admin menu in your WordPress Dashboard -> Settings -> SolidWP Licensing, and on that page, enter your SolidWP username and password. If needed, you can reset the password by going to the Member Panel login page and clicking the "Forgot password?" link.