Archiving requires Admin access. If you can't perform these steps, ask your account administrator to do it for you.

Archiving removes a case from your active list without deleting it — an archived case stays viewable and can be restored later.

On the case screen, click the pencil (Edit case) icon next to the case name to open the Edit Case window, then click Archive Case at the bottom.

Click Yes to confirm. As the dialog notes, once a case is archived it can only be reached again by restoring it from Account Settings, a restore can take up to 24 hours, and it can be done once per month without incurring additional charges.

Open Account Settings → Organization → Cases, then click the Archived tab to list your archived cases (or use the search box).

Open the case you want to bring back and click Restore Case. Restoring can take up to 24 hours to complete.