Complex sentence: Her television debut, in 1938, was in a BBC production of "The Duchess of Malfi"; her last appearance, in 1973, was in the "Play for Today" installment "Mrs Palfrey at the Claremont".
Split into simpler sentences: Her television debut in 1938 was in a BBC production of "The Duchess of Malfi". Her last appearance in 1973 was in the "Play for Today" installment "Mrs Palfrey at the Claremont".