You can. By default, all your Clippboards will appear in alphabetical order. If you choose to reorder them, you just need to click the gear icon next to the My Clippboards header in the menu on the side of Clipparoo. A new layer will open with a list of all your Clippboards. Drag and drop Clippboards into the order you want. Your changes will automatically be saved, just close the layer. If you have custom ordered your Clippboards, all new Clippboards will appear at the top of the list (otherwise, they will appear in alphabetical order).
If you wish to return the list to alphabetical order at any time, just click the gear and then click the Alphabetize link at the top of the layer.
Please note: SubClippoards cannot be reordered, and will always appear alphabetically under their top level Clippboard.
Your Clippboards are divided into two major categories - My Clippboards,
and Collaborative. The Clippboards that you'll find in the
Collaborative category at the bottom of your Clippboard menu are the
Clippboards that belong to other Clipparoo members, who have invited you
to collaborate. Those Clippboards will be ordered under the name of the person who owns them, and you cannot reorder them.
If you want the Collaborative Clippboards to appear at the top of your Clippboard menu, you can change the order by going to your Account page (clicking the three bars in the upper right corner of the page and selecting Settings/Account). From the Account page, choose Settings & Notifications, and Default Order. You can then choose to put Clippboards being shared with you (Collaborative Clippboards) at the top of the menu, instead of the default, which is to see your own Clippboards (My Clippboards) at the top.