I've been learning for a while, but my teacher is moving away/I'm changing schools and can't have lessons there/...
No problem, these situations arise. I'm very familiar with helping pupils through such transitions as smoothly as possible. Come and meet me, show me something you can play already (don't worry, it's not an audition!), and if you're happy with how things go we can plan ahead for regular lessons.
It's been a while since I stopped lessons, but want to start learning again.
Great! Never mind that you've had a break, all that hard work from before hasn't gone to waste, we'll be able to build from where you'd got to, while maybe also bringing a fresh outlook to things.
I think I (or my child) would benefit from changing teachers.
Every experienced teacher recognises that not all teacher-pupil relationships work out well, plus some children find having lessons in school to be rather disruptive when it means missing other lessons and having to catch up with work. I've certainly been on either side of this exchange in the past.
If you're in this position, please be reassured that I'll treat it sensitively. I'm happy to meet with you and discuss the position you're in, and give you the chance to think things through and to discuss it with your present teacher (and perhaps other school staff, if you're having lessons there) before making any decision. My priority is that you move ahead in whichever way will help you progress with your playing and learning, and any discussions we have about your current situation will be treated with appropriate confidentiality.