Fork, in the GitHub context, doesn't extend Git.
It only allows clone on the server side.
When you clone a GitHub repository on your local workstation, you cannot contribute back to the upstream repository unless you are explicitly declared as "contributor". That's because your clone is a separate instance of that project. If you want to contribute to the project, you can use forking to do it, in the following way:
Check also "Collaborative GitHub Workflow".
If you want to keep a link with the original repository (also called upstream), you need to add a remote referring that original repository.
See "What is the difference between origin and upstream on GitHub?"
And with Git 2.20 (Q4 2018) and more, fetching from fork is more efficient, with delta islands.