Maths tutor of three years is moving cities in May. What do you look for in the next one?

She has had the same home tutor since she was seven. The tutor knows her, knows my on-call weeks, and adjusts without being asked. She's moving to Pune next month. Most of what I hear about replacements is about results. I care more about whether the person can explain one idea three different ways and notice when my daughter is nodding without understanding. How do you check that in a trial session? And did your child take long to settle with someone new after a long stretch with one tutor?