Someone who is learning a music instrument for pleasure alone, is it allowed to take music lessons during the period if sefirat haomer?
I believe Rav Nachum Rabinovitch, shlit"a, is meikil. (I believe Rav Yoshe Ber Soloveichik,z"l, was meikil regarding listening to music in general during sefira.) Similarly, Rav Belsky is lenient with regard to continuing music lessons during sefira:
Refer to opinions of Harav Elyashiv Shlita and Harav Korelitz Shlita quoted in Piskei Shmuos page 53, see Chut Shani Shabbos 4:page 379 who permits it if one is just starting lessons since it is not music.
However, the Tzitz Eliezer (Sh"t Tzitz Eliezer 16:19), even year-round is lenient only if it is not for pleasure (as one part of the year-round ban zecher l'churban (in commemoration of the destruction of the Temple). Furthermore, even if it is not for pleasure and even year round...
Kaf Hachayim 551:41 writes that preferably it should not be done, and even if one is lenient it should only be sad songs. Miyum Hahalacha 1:83, Emes Liyaakov 551:footnote 506 also say that it is preferable not to. The Pri Megadim Eshel Avraham 551:10 writes that parallel to the concept of davar ha'aved on chol hamoed, the rabbis permitted somebody who needs to dance or play music for livelihood to do so. )