In order to upgrade from Free to Pro Plan, please remove the Smart Checklist Free add-on from the "Manage add-ons" Admin section and install Smart Checklist Pro from the Marketplace.
All your data i.e. created checklists or templates are safe and will not be removed. They are stored on your Jira instance.
Go to "Apps" through Settings
Go to "Manage apps"
Find "Smart Checklist for Jira. Free"
Go to "Find new apps"
Type "Smart Checklist for Jira. Pro"
Install the newest version
You are all set!
Continue using Add-on with enhanced functionality!