Docker Registry could be useful in various scenarios, but the most common would be containers orchestration software such as Kubernetes, OpenShift/OKD or Nomad. In example environment you could have Gitlab CI pipeline configured to build Docker image and push it to your registry and then let orchestration software to deploy it to a cluster.

In order to install internal, private Docker Registry you need to install Docker package first.

sudo apt update
sudo apt install apt-transport-https ca-certificates curl software-properties-common
curl -fsSL https://download.docker.com/linux/ubuntu/gpg | sudo apt-key add -
sudo add-apt-repository "deb [arch=amd64] https://download.docker.com/linux/ubuntu focal stable"
apt-cache policy docker-ce
sudo apt install docker-ce
sudo systemctl status docker

Then you need to grab certificate and start docker registry container:

sudo docker run -d --restart=always --name registry -v /home/user/certs:/certs -e REGISTRY_HTTP_ADDR=0.0.0.0:443 -e REGISTRY_HTTP_TLS_CERTIFICATE=/certs/certfile.pem -e REGISTRY_HTTP_TLS_KEY=/certs/keyfile.key -p 443:443 registry:2

This way we start a registry container which will always be up and running. We bind it on port 443 so need to have valid certificate and key for the domain. You can create A record for either public or private IP address. Former is easier, but the latter would be more secure. Both ways no need to setup insecure registries configuration as it will be offered via TLS connection.

After setting up, just build, tag and push container image to this registry.