When making a scene in a story, does it need to be working with the plot or can I have a scene just to introduce a new character and what they do? Even if it has little to nothing to do with the plot? Because I really want to make this scene but I'm not sure because it's only purpose is to show the viewer a new character and what they do for the other characters. Is it okay to write this scene?
Everything's permissable in writing, though not everything is of benefit. When introducing a character it is of benefit to make the scene about who they are.
Scenes should progress the story. Establishing a character's background is often a vital part of a story, and as such is a suitable purpose for a scene.
Um, I think it's commonplace in books as well as movies. There is one scene where one important character does something, and then there is another scene where another character does something else, and it's not immediately obvious what the two have in common. And at some later point they get together and the connection will be made clear. From an avid reader's point of view, that's totally cool.
A scene to introduce a character is fine, but it should be clear that (s)he fits into the story in some capacity. I find that some of the most effective scenes are the ones that do more than one thing. Good luck. PS. In all cases, I would write the scene, then decide if it fits.
Character development does have benefits so a scene that brings readers closer to someone they are going to know about does have a benefit. I don't see it as a disconnect from the plot. People enter our lives in different ways. The same is true with characters and stories. I think it can be done without derailing anything.
Character is vital to the plot, so a totally-unconnected scene which shows it well can still be hugely beneficial. The 'Meeting Mobsters' scene at Satriale's in the Sopranos is a classic case.
If your character is important to the plot, then spending a scene to introduce them isn’t a wasted effort. I think you should try it and, as you write on, it may even give you ideas on how to tie it back to the plot.
Lot of great suggestions here. If I was in this situation, I'd write the scene and figure out how I could tie it into the story in a fluid manner. And if it absolutely doesn't work for the whole of the story, at the very least I've learned a few things along the way. Let us know how it goes! Edit: Maybe this thread will help https://www.writingforums.org/threads/how-to-tell-if-a-scene-moves-the-plot.163267/