You have to be either an Account Owner or a Workspace manager to be able to archive Workspaces in your account.
1. How to Archive a Workspace?
To archive a Workspace along with its belonging boards -> click the Workspace Settings icon (the three dots icon) of the corresponding Workspace and select Archive Workspace.
A pop will appear with a summary for the Workspace and the Boards you want to archive (Img.1).
Important: If you are an Account Owner or a Workspace manager you might not be seeing all of the boards in a given Workspace. Nevertheless, if you archive a Workspace, all Boards in that workspace will be archived irrespective of whether you are assigned to them or not.
Click the Archive button to trigger the archiving.
2. How to unarchive a Workspace?
All archived Workspaces in your account are stored in the Archived Workspaces and Boards panel of your account and you can access and restore them anytime.
Go to the Dashboard of your account and select the icon "Show Archived Workspaces and Boards" located right to the Filter at the bottom of the Dashboard.
To restore an archived Workspace, you need to unarchive at least one of the boards that belong to it.
In the Archived Workspaces and Boards panel, please select the Unarchive icon of any board that belongs to the Workspace and it will be restored to your account along with the board.
You can use the Filter options to quickly search for a Board name.
The unarchived Workspace will become available on your account Dashboard.