The Design 'tab' is known as a menu.
Menus form part of your command layout scheme. You should open your work environment dialog and Apply a stored scheme that contains the Design Menu.
Do this under the 'Command Layout Schemes'.
Alternatively, if you don't want to apply a whole new command layout scheme (which also includes toolbars and context menus) you may have to rebuild your current scheme to include the Design menu and all its items again.
Cheers,
Link.