JUL 'MDAMA’S COVENANT
'Mdama was by far the most successful former Covenant member to command a fleet and uncover Forerunner artifacts for his advantage. Jul's motivations stemmed from early in the post-war era, when he was captured by the Office of Naval Intelligence, and his wife was killed during fighting with Thel 'Vadam's forces on Sanghelios. After 'Mdama managed to escape from ONI's grasp, he found a fundamentalist group of Sangheili and proceeded to recruit them on his quest of revenge.
'Mdama and his forces then managed not only to build a formidable fleet of former Covenant vessels, but used the knowledge of the Forerunners he had collected to locate the Ur-Didact's shield world, Requiem. On Requiem, Jul 'Mdama was able to recover the Janus Key, a Forerunner device that could point the way to every Forerunner artifact in the galaxy. While he only made off with half of it, he also managed to kidnap Doctor Catherine Halsey and use her knowledge to help strengthen his fleet.
After Requiem, 'Mdama's forces used covert tactics to recover the second half of the Janus Key and traveled to the Absolute Record to try and open its secrets. Jul was nearly successful, but ultimately failed and lost the Janus Key. He then attempted to make a recovery and continue uncovering more Forerunner secrets, but was found and assassinated by Spartan-IV Fireteam Osiris on the planet of Kamchatka in October 2558.
SWORDS OF SANGHELIOS
The last Covenant Arbiter, Thel 'Vadam, and his Sangheili allies were instrumental in helping the UNSC win the Human-Covenant War. Once the war ended, he quickly tried to cement his political and military power at home, but faced stiff resistance from many Sangheili groups who didn't like 'Vadam's newfound alliance with the humans. It was that very alliance, however, that ultimately allowed the Swords of Sanghelios to emerge victorious over all other former Covenant factions late in 2558.
KEEPERS OF THE ONE FREEDOM
In 2553, Castor, a Jiralhanae Chieftan and Dokab of the Keepers of the One Freedom, led a pack of Brutes onto the human colony world of Gao and attempted to take control of a Forerunner ancilla located within one of the cave systems of the planet. Although he had help from insurrectionists on the planet, Castor's plans were thwarted by the actions of Spartan-II Blue Team, as well as a handful of Spartan-IIIs and the UNSC 717th Xeno-Materials Exploitation Battalion.
Later in 2553, the Keepers' base of operations was nuked by the UNSC after a kidnapping was staged to appear to be carried out by the Keepers rather than the actual perpetrators, Dark Moon Enterprises.
SERVANTS OF THE ABIDING TRUTH
As soon as the Human-Covenant War ended, there was a struggle for power on Sanghelios between the Arbiter Thel 'Vadam and those who opposed his idea of ceasing war with the humans. One of the first and strongest factions to rise to power were the Servants of the Abiding Truth, a deeply religious group led by Avu Med 'Telcam who still revered the Forerunners as gods. Their actions early in 2553 nearly toppled the then fragile rule of Thel 'Vadam, and likely would have succeeded were it not for the intervention of the UNSC Infinity in support of 'Vadam. The Servants were forced to flee to the former human colony world New Llanelli, where 'Telcam was eventually assassinated in 2558.
When the Great Schism ripped the Covenant apart, most of the San'Shyuum, aka the Prophets, fled and were not heard from again. One exception was The Minister of Preparation Boru'a'Neem and the Prelate Tem'Bhetek, who devised a plan to strike at the Sangheili in 2553. Using Tem'Bhetek's superior strength and intelligence, they led the CAS-class assault carrier Shadow of Intent, commanded by Half-Jaw Rtas 'Vadum, into a trap with the intent of killing everyone on Sanghelios. The plan was nearly successful, but was thwarted through the actions of Rtas 'Vadum and his crew.
In 2554, a Sangheili Zealot by the name of Merg Vol had gathered up a large fleet of former Covenant vessels and followed the word of a Forerunner oracle to the moon of human colony world of Draetheus V. There, Merg Vol found not just a human presence, but a Forerunner device capable of destroying planets. While Merg Vol's forces did manage to gain control of the device, known as X50, the actions of Spartan-IVs Sarah Palmer and Edward Davis along with the UNSC forces stationed at the colony, were able to stop Merg Vol and his forces from destroying the planet.
OTHER COVENANT REMNANTS
There have been several events in the Halo universe that have not yet been pinned on a specific faction or group formerly associated with the Covenant. These attacks, while seemingly random, are no less destructive than those perpetrated by any known group.