Docker pull then start for running container – what is the expected behavior?

Let’s say I have a running Docker container X that is based on image foo.

If I pull a new version of foo, then stop and delete X, and then docker run foo – will it have the new version of the image?

Said differently – do I need to stop X before I can pull the new version of foo and then start it?

The context is Docker-EE on Windows Server 2016.