Restrict Access
Deep Clone for Jira supports restricting access without changing Jira user groups.
You can configure Deep Clone for Jira specific restriction under Apps > Manage Apps > Deep Clone > Restrict access.

If Restrict access is enabled, but no projects are configured, no user will be able to select a target project.
Restrict Cloning Into Certain Projects
Check Restrict access to user-groups
Select the project in the drop-down you want to restrict cloning into
Select group(s) that should still be allowed to clone into this project
Save
Users need to have the “Create issue” permission for this project in order to be able to Deep Clone into it, regardless of the “Restrict access” settings below.
Restrict Other Deep Clone Features
Disable cloning attachments
Disable cloning comments
Disable cloning work logs