music teacher leaving county music service, but continuing to teach at school

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Just been told that DC's county music teacher is leaving the music service, but the school is taking them on as a private teacher. So we need to cancel lessons, then pay the teacher directly after Christmas.
Is this common? Should I be worried? Any red flags? It just feels a bit weird to me.

Perfectly normal. They are justvbe8mg paid directly rather than paying an additional fee to an agency

I think any issues will be between the teacher and the music service. Some music services have been making people redundant and having an increasing amount of their teaching on an agency/self employed basis, so it could be teacher had no choice. Others have contract clauses that say if they leave the service they can't take on the same pupil within a 3 month window or something, to try to prevent teachers jumping ship with all their pupils.

But whatever is going on on that side is between teacher and music service, not your problem. Our primary and secondary schools (state) have both private and music service teachers and from a pupil perspective it's just different admin.