Is it possible to add extra setting tabs to the admin panel for the board?

Do you mean adding a menu item with a link to the ACP? If so, yes. Add it as you would any other menu item using System > Site Features > Menu Manager.

Or do you mean adding extra tabs to the left hand menu within the ACP? If that's what you mean, this is done in the developer center for an application under "Admin CP Menu". When you add a menu item you just specify the menu tab to the new tab. You then specify language strings to set the icon and the label.

• menutab__{$tab}
• menutab__{$tab}_icon