Is there a technique or a better method to place a mesh..

Is there a way to easily place a mesh on top clothes without there being a gap in between the mesh and clothes? 

I made this shape and I'm struggling to adjust it to this part of the arm. 






I want the patch to look like this but no matter where i move it or how i rotate/adjust one end of it is floating and doesn't look like it's been stuck onto the clothes




If anyone could give me any pointers. I'm new to Blender so learning along