GitHub stream after receiving

I have a repo on GitHub (Enterprise, for what it's worth) that I am using for my application. I also have this application deployed to a development server on the same network. I read the Git scroll and I registered my server url in the WebHooks section of the repo on GitHub. However, I don't know how to set up a fetch trigger that every time commits are pushed to the repo, I want the server to fetch JSON data from POST, update the web app repository (web app is also under Git) with the data and restart some services.

How can I do the above in the simplest and easiest way?

Thank.