How to auto-update containers using CI?

Question

System administration

Good afternoon!
How to automate the update of already running containers on a Prod machine via jenkins CI?
At the moment I see the scheme like this:

Code development
->
Private Git repo
->
Jenkins Docker image build
->
Private docker regestry
->
???
->
Update prod docker container

Those. I would like, after pushing to our repository, jenkins would collect the image, publish it to our private register, and then, the prod machine would pick up these changes and restart the containers.
Since there is little experience in this matter (I'm not a real admin, but DevOps), maybe I'm saying something wrong, and there is already best practice in this matter.
Also interested in how to gracefully reload such containers on production machines?

Answer 1

https://habrahabr.ru/company/hexlet/blog/258815/