Is it possible to add a mixamo animation to an existing rigged character?

I recently downloaded a character that is already rigged with a mixamo rig but how would I go about parenting an animation from mixamo to this rigged character?

Yes its called retargeting. There are a bunch of tutorials for it.

Hey there, you can either upload your rigged character to Mixamo and have animations applied through the website, or if you want to apply the animation in Blender instead, we provide a Blender plugin for Mixamo to help with retargeting and setting up animation controls for Mixamo rigged characters so you can continue to add your own flourishes to the animation data

Hope that helps!