He soon began taking lessons from Vincenta Tormo de Calvo (Madrid Conservatory faculty) and Luisa Menarguez.
Then he travelled to the U.S. and there, on July 5, 1934, he made his North America debut in New York City.
[4] During the years of 1959–1962 he led a harp class on Accademia Musicale Chigiana courses in Siena.
[2][6] People who composed for him include Alberto Ginastera, Darius Milhaud, Germaine Tailleferre, Xavier Montsalvatge, Heitor Villa-Lobos, Walter Piston, Ernst Krenek, Joaquín Rodrigo.
[4][6] Josef Tal's Concerto for Harp and Electronics was commissioned by Zabaleta in 1971, and premiered by him in Munich the same year.