If you are a Professional in Music, How to advertise private music lessons?

As you are a professional in music, then I suggest you to upload the video on YouTube, which shows his talent and who are interested can contact you.
 
You can also
 
Something to promote with the help of the Network of Social Media. Social networks play an important role in the promotion. So in conclusion, it is probably better to put your information in the free local online directories in your city or county, then consider the boards of registration.
 
Finally,
 
Consider an entry in Yahoo Local for a flag appears on a map of the city that shows where, if someone does a search on Yahoo, for example, music teachers in their city. See the link below if you want to add to Yahoo Local UK. And the same for other search engines. And maybe a card appears on all local music stores that sell instruments and on the boards of the local university.