I have to give it to you, this is one random Tasha question.
For the record, she left near the end of the first season, not the second.
I'm not 100% sure that there never was a scene written in which she played a musical instrument - I'm only 99.89% sure. She was more of a fighter than an artist, and I don't see her on Turkana IV - taking a break from all that running away from rape gangs by having piano lessons.
To answer your other question, Picard also played the flute in A Fistful of Datas
, and Riker played the Trombone in Second Chances