What is the proper way to create an extension to a plugin?

I am extending an existing plugin, but I’m still a beginner to all this. Basically, I’d like to create an extension to this plugin (all of my code outside of the plugin’s code) so that when I can still download the plugin’s updates without needing to re-edit all the code. I know there could potentially be a ton of changes with their updates, but here’s to hoping.

How do I properly begin to create this extension? How does code qualify as an extension of a plugin and not a plugin itself? Or does it actually have to be a stand-alone plugin? I’ve started to write code for this but my localhost isn’t recognizing common WP functions like add_action, so I’m thoroughly lost.