Complex sentence: In 1951, while Klein was studying for his Masters degree in Columbia, Missouri, Welk and his orchestra came to St. Louis, Missouri, for an engagement and encouraged his cousin to try out for his band, which he accepted.
Split into simpler sentences: In 1951, while Klein was studying for his Masters degree in Columbia, Missouri, Welk and his orchestra came to St. Louis, Missouri for an engagement. Welk encouraged his cousin to try out for his band, which he accepted.