Complex sentence: Peary switched to CBS, while the program in which he had starred, "The Great Gildersleeve", stayed on NBC, resulting in a new program ("Honest Harold ") for Peary and a new star (Willard Waterman) for"Gildersleeve".
Split into simpler sentences: Peary switched to CBS, while the program in which he had starred, "The Great Gildersleeve", stayed on NBC. Those changes resulted in a new program ("Honest Harold ") for Peary and a new star (Willard Waterman) for"Gildersleeve".