Navigate to the “Global Permissions” within the Jira System settings (Settings > System > Global permissions).

At the bottom, you will find

A user with these permissions will be able to access Deep Clone for Jira for all issues in all projects, no matter how project permissions are configured. All users have the Single/Epic and Bulk Clone permissions by default.

The Project Clone permission is given to all administrators by default, but can be extended to other users as well.