You can partially automate this using Git.
Clone your repository on your machine, then modify your jupyter files from there. Git automatically tracks changes. You have only to commit them and push to GitHub.

If you want to completely automatically update your changes to GitHub, a solution could be to create a script which runs periodically looking for changes: if it detects any modification, it automatically commit, with a standard message, and push to GitHub.

Working on Windows this answer could be useful for compose a python script which periodically checks file changes (you can do this comparing last modification date), then this tutorial could be helpful to make the system able to run the script at every startup on Windows.
If you are working on Linux you can use this tutorial to find how to run scripts on startup on your system.