Find someone who can spark your child's interest
If you want to really learn a language and be fluent in it, you have to study it throughout your whole life, constantly practising it and improving. That is only possible if you find it interesting and enjoy having lessons. Which is why you should pay attention to how good the teacher is at motivating their students. Can he make the lessons entertaining? Does he know how to keep the child involved in the process throughout the lesson? Of course, some kids are shy and will need some time to get used to their tutor, but these things should become clear after the first couple of lessons.
Take into account your child's interests and temperament
In order to make the learning process productive and encourage your kids to have regular lessons, you should make sure that they have something in common with the teacher, both in terms of interests and temperament. If your child is calm and a bit timid, it's better to go for someone who will give them an opportunity to open up, without putting them under too much pressure. If on the contrary your kid is active and energetic, look for an enthusiastic teacher that will make sure each lesson is dynamic.
Allow your child to get used to it
It goes without saying that you should always hear what your kid has to say and try to take their wishes into account. But it's also good to remember that most children need some time to get used to having regular lessons with a new teacher. That's why you shouldn't jump to conclusions after the first lesson. Give it some time. But if after the first 4 or 5 lessons your kid still doesn't like it, then you should probably look for other options.