A new student arrives with several years of lessons behind them. Their fingering looks unusual, they use a different term for an exercise, and the bow hold isn't quite the one you teach.
You could spend the first month changing all of it. First, hear what they can do with it.
Let them play something they know
Ask for a familiar piece and give them a chance to settle. Listen for the musical result as well as the technique. Can they keep a pulse, shape a phrase, and recover after a slip? Which parts sound comfortable?
Ask how they practiced the difficult section. Have them demonstrate the method instead of relying on a description of what their old teacher said.
The student may have a useful strategy expressed in unfamiliar language. Find out what it means before replacing the vocabulary.
Choose the changes that have a reason
A habit that causes discomfort needs attention. So does a technique that repeatedly prevents the student from reaching the sound they want. A different fingering that works reliably may be less urgent.
Explain the reason for any change and demonstrate what you hope it will help. Then compare attempts together. Give the student time to learn the new movement, and check comfort rather than insisting that unfamiliar must mean correct.
Avoid changing several major habits at once unless there is a clear need. Otherwise the student can lose familiar ways of playing before the replacements are usable.
Keep the previous teacher out of the argument
You weren't in those lessons. You may be seeing an unfinished process, an adaptation for a particular problem, or something the student misunderstood.
“Let's try this fingering for the faster tempo” gives you room to teach without announcing that the previous instruction was bad. If you need more history, ask the family whether contacting the former teacher would be appropriate.
Keep a few familiar pieces while introducing your approach. Those pieces give the student somewhere to play confidently during a period when other things may feel unsettled.
Agree on the first month
Choose an immediate goal together and say what you plan to leave for later. After a few lessons, ask which changes are helping and which still feel confusing.
Your first job is to understand the player you've inherited. There's time to develop your way of working together. The First Lesson With a New Student has a structure you can adapt.