My teacher does that all the time.
One of my teachers used to end the formal lesson at the scheduled time. After that she would offer to show me some music: "Have you heard this before? I'll play it for you then." Sometimes these sessions would go some 30 mins past the lesson ending time. She would just pull music off the shelf, give an enthusiastic introduction to the piece, then proceed to play it. No extra payment was ever required, and I never complained. I was so grateful that she would freely give her time to sharing all this music with me.