To use this functionality you need to set-up "Checklists" custom field.
Not available in next-gen projects. Please see the details here.
When the "Checklists" custom field is added properly and assigned to the necessary project screens - checklist content will be cloned upon the "Clone" procedure from Jira Issue.
Example:
Error rendering macro 'excerpt-include' : No link could be created for 'Support'.