Most private teachers get pupils through word of mouth, a school noticeboard or a recommendation in a local parents group. What happens next is predictable: the parent looks you up. If they find nothing, or an old listing with the wrong phone number, the recommendation loses a lot of its weight.
What they are hoping to see is fairly simple. Which instruments you teach, whether you take beginners and what ages, where lessons happen, what a term costs, and whether you prepare pupils for graded exams if that matters to them. Parents of younger children will also look for your safeguarding arrangements, such as a DBS check.
Adult learners read differently. Many are returning to an instrument after years away, or starting from nothing, and want reassurance that lessons will be relaxed. A good site speaks to both groups. We build it, host it and make your changes each term.