I'm new to Inkscape, and I'm working on a project where I want to merge these two shapes in such as way that that green shape fits in the yellow one and all the excess stuff gets removed. I have included some photos to explain what I'm, trying to say.
Your question isn't very clear, however it sounds like a clipping mask is what you are looking for.
For it to work, the shield shape needs to be a single closed path.
Move the green shape over the yellow, into position.
Copy and Paste in Place the yellow shape.
Select both shapes and click Object > Clip > Set