Ha’Rav Ovadyah Yosef (a”h), states that if a person earns a living by giving music lessons, he may continue his work during the Three Weeks, until the week of Tisha Be’Av, in order to avoid a loss of income. Once the week of Tisha Be’Av begins, he should refrain from teaching music.
On the basis of this ruling, we may conclude that during the Omer period, when music is generally forbidden, a professional music teacher may give music lessons. Just as during the Three Weeks period – a teacher who will lose income by refraining from giving music lessons may indeed continue giving lessons during the period of Sefirat Ha’omer. This is, Rav Ovadyah Yosef’s ruling in his sefer Yalkut Yosef.