The lessons are an ongoing expense, but the principals will rather quickly eliminate the middle man marketplace after meeting and being happy with the connection.
Unless you can provide other useful services to help the teacher to manage thier students. Maybe scheduling, accounting, payments.
In that case it seems a lot easier to skip building a marketplace and just create booking software for music teachers.
Though you'd probably find that most were happy with Google Calendar, Xero and PayPal / Square.