It seems to me that the tool you're looking for is the [Pathfinder][1]. The Pathfinder allows you to combine objects in different ways, be it merging them into one whole or, like in your case, subtracting a shape from one behind it. You'll most likely want to use the "Minus Front" option. What this will essentially do is punch a star shaped hole in the shape below it. Just make sure your paths are arranged in the correct way (so that the star is on top) in your layers panel.

#Before:

![Screenshot of the Pathfinder tool being used in Illustrator CC 2014][2]

#After:

![Screenshot of the results of the Pathfinder tool being used in Illustrator CC 2014][3]


  [1]: https://helpx.adobe.com/illustrator/using/combining-objects.html
  [2]: https://i.sstatic.net/RfUgI.png
  [3]: https://i.sstatic.net/XfFpY.png