New Category

Is it possible to suggest a new category and apply to be editor for that category?

No. You have to apply to an existing category. After you're an editor you can always gather a bunch of sites together in your internal Bookmarks area for the category that you think needs to be created, and then suggest the new category in the internal forums. If there is a group consensus that the category would be worthwhile, it can then be moved out of your Bookmarks and into the main directory with you as the editor.

It is, however, possible to apply to an existing category like Science/Useless/Widgets, and in the "remarks" field say "I'm really only interested in Ordovician widgets: I notice you have one site already that focuses on Ordovicianicity in Widgetx (xxx.ordowidget.com), and here are three more. I've got a list of a dozen or so other sites, which I would like to add, and I'd suggest a new subcategory for them."

The meta CAN create that category, and accept you into it. It does happen occasionally: the current Hymns editor <img src="/images/icons/wink.gif" alt="" /> started out that way.