After the Wars...
Fairfax had quarrelled with Cromwell over the execution of the king and withdrew from active politics, leaving Cromwell to manage the business of government and mediate between increasingly hostile factions in both the House and the Army. In 1653, irritated by its self-serving interests and slowness in developing solutions for the Commonwealth, Cromwell disbanded the Rump Parliament. In the process, he refused the crown but was proclaimed Lord Protector. History documents that he did a good job governing the country, steering it through war with the Dutch and helping Portugal gain independence, although he still faced opposition in England and especially in Ireland. He died of malaria in 1658. What happened next, and the move towards the Restoration of the Monarchy, is another story.
NB: This aims to provide a simplified uncomplicated timeline of the wars. For almost every aspect here you can read more detailed publications exploring the battles, people, philosophy and politics. Ours is a fascinating period which should give you hours of endless fun digging for information and viewpoints.