Complex sentence: His London debut was at the Palladium in "Band Wagon" (1939), and his New York debut was as Captain Worthy in "The Relapse", as part of the Theatre Guild (1950).
Split into simpler sentences: His London debut was at the Palladium in "Band Wagon" (1939). He made his New York debut as Captain Worthy in "The Relapse", as part of the Theatre Guild (1950).