If it’s already made and rendered, then really isn’t a tutorial for doing that. Also, if you could post a screen capture of what you have, it would help in coming up with solutions. That being said, one method would be is drop the video into a comp and duplicate it. On the bottom layer, you where the arm is located, you would need to paint the background over the arm. On the top layer(s), you would mask the arm(possibly multiple layers, masks if you want it to bend at the arm/shoulder/wrist). Then you would animate the different layers to move it.
Here is a tutorial that gets a little into painting back in a background that.
Virtual 3D Photos
A link to basic AE techniques, masking, keyframing.
Video Copilot Basic Training series
Also, without seeing your gif, you might be able to use the puppet tool, so you might want to to google After Effects Puppet Tool Tutorials.
Johnny Cuevas, Editor
ThinkCK
“I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work.”
—THOMAS EDISON on inventing the light bulb.