story mode

Yes, you have to start a new game save. But what you can do if you don't want to start a new game save is this.

Start a new game save to get the story mode. Go through all the questions, and after that do what you want to your sim. Then save your sim(s) in your library. Exit back to your main menu, don't save. Then go to the game save you were playing, and you can then take that sim from your library and place them in your current game save. All their information will still be there.

thank you

You can make a story Sim in an existing save and even in an existing household.
When you create a new household in an existing save the story mode doesn't pop up automatically, it gives you a random Sim like before, however you can add a new Sim with a story, just need to choose the option with book icon.
https://i.imgur.com/NNtNCCC.jpg
It works in an existing household as well, as you can see.
However note that the wealth amount that the quiz gives you overrides the existing household funds.