Click into Tools & Settings:
Select Users > User Groups
Scroll down to User Group Privileges
Here, you can choose whether a user group can have access to clearing a longlist's search results
Things to keep in mind:
*The only way to recover a longlist that was cleared is by re-running your search
*If you choose to check this privilege off, then you can track what users cleared a longlist in the Longlist Audit History.