I would like to know if there\'s possibility of deployment (Website) on a prod server with GIT?
Let me explain:
I have a team who work locally, it working with G
You would need, with gitlab, to use a webhook (same idea as with GitHub), in order to trigger a git pull from your prod environment.
See an example of a Gitlab webhook at "How to setup Gitlab with post-receive hook?".
Note: that webhook doesn't have to be in php: you can see more details and a different example in "Jenkins Gitlab Hook Plugin".