Complex sentence: Wolff had been the music director for jazz singer Nancy Wilson, who then introduced him to Arsenio Hall; this prompted Hall to choose Wolff to conduct the orchestra on "The Arsenio Hall Show".
Split into simpler sentences: Wolff had been the music director for jazz singer Nancy Wilson, who then introduced him to Arsenio Hall. After Wilson introduced the two together, Hall chose Wolff to conduct the orchestra on "The Arsenio Hall Show".