How can I make an image appear partially in front and partially behind another layer in Adobe Illustrator?

"I had a similar issue recently (trying to Photoshop someone into a scene!)

After looking around for ages, I was told that it was due to ""Layer Masking"", I am trying to find the article that helped me, (It was for Photoshop) but until I do, I just had a quick look for Illustrator and found this page -

This should help you, but I will try to look for a better answer and edit this if I find a more specific one."

"You could make the paw a separate object on a layer above the circle or alternatively you could use a clipping mask.

I would recommend using a clipping mask because it is 'non-destructive' in the sense that you can still move around your pieces without having to butcher any of your shapes.

Make your Orange punched-out circle shape.
Make your paw (and the animal attached to it) and position it above the circle (the whole thing will be popping out, but don't worry.)
Make a new shape that encompasses the paw/animal (the shape is unimportant for now - just make a big green blob or something)
Highlight the blob and the shape together and choose Object > Clipping Mask > Make (shortcut is cmd 7) The blob will become an invisible Clipping Mask which will only let the objects grouped with it to show up underneath wherever the blob goes.
Now in the layers menu expand your layer with the dropdown arrow so you can see all the shapes. The new ""clipping mask"" you just made will be a group. Expand that group. Highlight the clipping mask inside the layer menu by clicking the circle to the right of the label ""Clipping Mask.""
Now use your tablet (or mouse) skills and reshape the 'blob' to cover up the part of the animal that you don't wish to show.

Clipping masks are a complex subject, but I use them for stuff like this all the time. Even a cursory glance through the Clipping Mask help in Illustrator should be able to fill in any of the gaps. Good luck!"