You could do it with scripting, but poor man’s route would be to simply nest (pre-compose) the “clip” you created. You put the clip in a nest, then treat the nest as a single “clip” that you can use anywhere. (The nest also appears in your project window as a new comp. You can put comps within comps). Make sense?
If you want to loop, then you can do a nest within a nest. Put the animation in a nest, then loop that nest by duplicating it several times and butt end to end. Then you can nest all THAT in order to have a single “clip” available that contains your animation looping. Make sense? You can always go back and edit the the original nested animation anytime.
To create a nest (aka pre-compose it), select the layers of the animation you want to use as a clip and then select “pre-compose” from the layer menu.
Hope something is useful here!