Private Registry automatic download

Let say I have Docker Private Registry created

# docker run -d -p 5000:5000 --restart=always -v $HOME/registry:/var/lib/registry registry:2

and I am using it to supply the image vulnerables/web-dvwa locally.

Is there a way for this private registry to automatically detect and download if there is newer version of the vulnerables/web-dvwa image?

In other words check on Docker Hub and comparing with the version in my repository, then update the repository from it?

Source: StackOverflow