Complex sentence: Despite the debacle of his failed election as Speaker, he played an active role in the Parliament of 1613--5, and was readmitted to the King's Inns, at the request, perhaps surprisingly, of Lord Deputy Chichester.
Split into simpler sentences: Despite the debacle of his failed election as Speaker, he played an active role in the Parliament of 1613--5. He was readmitted to the King's Inns, at the request, perhaps surprisingly, of Lord Deputy Chichester.