After purchasing a license from the cPanel Store for CloudLinux, you need to install it. There are multiple ways to do so, but the fastest way is to use CloudLinux's instructions. They are provided below.
First, verify that your license purchase has gone through and has been issued.
Navigate to our license verification page and enter your server IP address.
On the next page, you'll want to see a large CloudLinux logo:
License History for SERVER-IP
|#||IP||Package||Partner NOC||Activity||Product||Status||Updates Expiration|
|active on DATE||CloudLinux||active||N/A|
Once you have verified that your license is active, log into your server via SSH and execute the following commands:
# wget https://repo.cloudlinux.com/cloudlinux/sources/cln/cldeploy
# sh cldeploy -i
A reboot is required to boot into the newly installed CloudLinux kernel and finish the installation.
CloudLinux has a further explanation of their install process available here.