Getting tab submenu links moved


So, I've been trying to figure out how to do this for quite a while now, but so far I haven't gotten anywhere.

What I'm trying to do is to take the links usually shown in the bar right below the tabs (and in the dropdowns) shown in a block in the right hand side, of course updating to display the correct links depending on what node you're on, as so that add-on's who utilize it will still get their links displayed as well.

Does anyone have any idea how I could achieve this?