Complex sentence: After his retirement from radio, Casey revived his father's variety act with Roy Castle and Eli Woods to great acclaim on "The Michael Parkinson Show" on BBC television in 1982, they were invited to appear in that year's Royal Variety Performance.
Split into simpler sentences: After his retirement from radio, Casey revived his father's variety act to great acclaim with Roy Castle and Eli Woods, on "The Michael Parkinson Show" on BBC television in 1982. As a result of that appearance, they were invited to include the act in that year's Royal Variety Performance.