Complex sentence: Richard Cromwell was the successor to his father Oliver Cromwell, but he gave up his position as Lord Protector with little hesitation, resigning or "abdicating" after a demand by the Rump Parliament.
Split into simpler sentences: Richard Cromwell was the successor to his father (Oliver Cromwell). But he gave up his position as Lord Protector with little hesitation, resigning or "abdicating" after a demand by the Rump Parliament.