How to render static and animated objects separately to save render time? I want to create an animation with 60 frames with two objects only one is moving. How to combine the rendered 60 frames of the moving object to 
the only once needed rendered fixed object. In short : render only what is changing.
So.. You should use 'View Layers' (https://docs.blender.org/manual/en/latest/render/layers/layers.html).
As said above in the comments by @Bruno you should render the still as an image, on the other view layer render the animation with shadow catcher and in the video editor (VSE) add them together to a video.

(to be honest you can probably just render them separately and attach them together later in the VSE just as long as you keep original scene.)

I am attaching link to a demo scene, hope it helps. (https://drive.google.com/file/d/10fXBH4o2sz4b0ceBPyRouquxhjgi_8gZ/view?usp=sharing)