Where will the planned Deep Space Atomic Clock orbit "after" Earth?
&quot;The instrument will be tested in Earth orbit for one year, ...&quot;
What would it then orbit?

It will continue to orbit the Earth, at least for a while. It will eventually end up not orbiting the Earth because it will be placed in low Earth orbit, where orbits decay due to atmospheric drag.
The project is a technology demonstrator, which means a limited amount of funding.