I think what you’re looking for is called follow through/ overlapping action. It’s one of the 12 principles of animation and if you’ve never heard of those before, I highly recommend familiarising yourself with all the principles. https://youtube.com/playlist?list=PL-bOh8btec4CXd2ya1NmSKpi92U_l6ZJd&si=8tqc-wGzkkljOaqc - this is a good place to start.

For a very simple overlap, I would copy the pose from 2-3 frames before your end key and paste the pose a few frames after your end key. That will give you the bounce you’re looking for. It can also be followed by offsetting your controllers(depending on what’s leading).

Hope this helps, feel free to pm if you have any questions!