Cambridge Dictionary says this definition of square is old-fashioned:
a boring person who does not like new and exciting ideas.
Then, what's another non-old-fashioned word or phrase for it?
Postscript: I might have found a synonym for 'square' now- it's 'puritan'. Not sure if this word is common enough, though. Cambridge Dictionary gives the following definition.
someone who believes that it is important to work hard and control yourself, and that pleasure is wrong or unnecessary
Background of my question: In a comedy, a middle schooler from heaven is sent to earth to learn about human. But living on her own, she instead indulges herself in video games so much that she skips classes and never cleans her room. When she knows that her elder sister is visiting, she shivers in scare. She explains that her sister is a sqaure, serious and strict, so she is fearful of the outcome of her degenerate life being found out.