I am currently rendering an animation in cycles and I have another animation to render after it is finished. I am rendering the current animation with my GPU and was wondering if I could render the other animation using my CPU in another instance. Would this be efficient? Thank you.
Yes, mixing CUP and GPU rendering on two instances should be faster if you have enough memory to fit two instances of the rendering job. Just make sure you set the CPU rendering instance to a lower priority (using the task manager on Windows, or nice with Linux) so that it doesn't take any CPU resources away from the GPU instance. Otherwise the GPU instance might be starved for instruction from the CPU and cause a slowdown.
With Blender 2.79a, a built-in mixed CPU/GPU rendering mode is also available. Just need to enable it from the User Preferences: