A LITTLE more than three years ago she was a quiet, serious-minded 16-year-old flutist in the West Bank with posters of the Berlin Philharmonic flute soloist Emmanuel Pahud on her bedroom wall. Travel restrictions made it a struggle to go for lessons in Jerusalem. Finding space to practice in an apartment crowded with four siblings was difficult. Despite her hard work, her prospects seemed limited.

But teachers from Israel and an outside foundation recognized her talent and gave her lessons. She was the star performer at a West Bank master class taught by none other than Mr. Pahud.

Now the young woman, Dalia Moukarker, is on the cusp of a rare opportunity: the chance to study music at an important European music school. The conservatory of Karlsruhe, Germany, has offered her one of four spots for flutists this fall, along with financial aid. As of last week, Ms. Moukarker had only to receive her German visa. If approved, she will become one of just a handful of West Bank Palestinians who have moved to the West to study as professional musicians.