School dance and piano lessons are two totally different poles. I'm not sure how you related the two as same.
However, if your domain has the word piano in it, it's okay to create a website around piano lessons as you have already mentioned.
Regarding the indexed links, you can resubmit the new sitemap in Google search console and inform the search engine about it. This way, your previously indexed pages will be deindexed in a day or two.
Hope this helps.