By default, only Jira administrators can manage Global Templates. To grant permission to other users go to Manage Apps → Multiple Checklists for Jira → Checklists Permissions
.gif?version=1&modificationDate=1664359971104&cacheVersion=1&api=v2&width=340&height=295)
Toggle the bar to allow Other users or groups and select users or groups of users to whom you would like to grant the permission.
After that, the selected users will be able to edit Global Templates and add Automation to them.