The end of the Human-Covenant War did not end conflict between species or even within species. Since the war was ended by the Great Schism, fighting between the Jiralhanae and Sangheili were initially significant and resulted in the destruction of much of the former Covenant fleets. As might of the Covenant faded, however, so did much of the conflict of the Great Schism. While the conflict never had an official end, most of the fighting had ended within a year of the end of the Human-Covenant War.
REBUILDING THE FLEET
Humanity, finally seeing a reprieve from decades of being on the defensive, used their unique position to recover the colonies they could and rebuild a fleet from the ashes. This fleet was led by a new flagship, the UNSC Infinity, which, while started eight years before the end of the war, was not battle-ready until months after, and not fully complete until 2557.
INTERNAL CONFLICT REEMERGES
Although the outer colonies had been largely laid to waste during the war, there were still a handful of colonies that managed to escape the wrath of the Covenant. Seeing their fight for survival come to an end, many of the colonists resumed what they had been doing before the war, namely rebelling against Earth rule. Lacking the force and manpower to wage a full-on war with the UNSC, rebel forces went back to guerrilla tactics and committed acts of terror in the name of freedom. With the rebels unable to face the UNSC directly, and the UNSC unwilling to instigate another all-out insurrection, small-scale conflicts continued for years.
A NEW CLASS OF SPARTANS
In parallel with rebuilding their fleet, the UNSC commissioned a new Spartan program to replace and build upon the Spartan programs of the past that had helped win the war. Deciding to use adult volunteers this time instead of abducting children, the Spartan-IV program created many more Spartan super-soldiers than the Spartan-II program ever did, and rivaled the output of the Spartan-III program. Though still significantly weakened by the loss of so many colonies and personnel, the UNSC was still able to use the newly created Spartans along with the UNSC Infinity to apply force when and where is was required.
After the fall of the Covenant, many leaders tried to take control of what remained and make their own place in history. The Covenant remnants were many, and lasted for many years after the fall of the Covenant. The Sangheili fell into civil war as their society that had been led by the San'Shyuum for thousands of years didn't have any natural leaders remaining to rule. Former Arbiter Thel 'Vadam and his Swords of Sanghelios quickly became the favorite to lead the Sangheili, but many different factions rose from the ashes of the Covenant to vie for power. While 'Vadam was considered the front-runner to rule Sanghelios within a year, conflict continued long afterwards, particularly with remnants of the Covenant led by rulers such as Jul ‘Mdama.
With the end of the war with the Covenant came an awakening of several Forerunner installations that had remained dormant since the time of the firing of the Halo array 100,000 years before. Among those awakened facilities was the Ark, whose monitor 000 Tragic Solitude held a grudge against humanity for the destruction caused on the installation's surface. This led to a series of events culminating in an attempted invasion of Earth, which was halted through the combined actions of the UNSC and Swords of Sanghelios.
Conflicts with Forerunner creations were left mostly to localized incidents until the discovery of Forerunner Shield World 001, or Requiem, in 2557. While both the UNSC and former Covenant under command of Jul 'Mdama battled in orbit and on the interior surface of the artificial world, the Ur-Didact, a Forerunner in stasis in a cryptum for the past 100,000 years, was awoken and attempted to complete his goal of wiping out any and all remaining humans from the galaxy. Though his plan was not successful, he did still manage to kill seven million people from the city of New Phoenix before he was stopped.