Covenant Loyalists
From Halopedia, the Halo wiki
The Covenant Loyalists are made up of the Prophet, Yanme'e, Kig-Yar, Jiralhanae, and some Unggoy castes within the Covenant's hierarchical society. This faction is made up of those who sided with the Prophets after the Civil War of the Covenant and since then has been fighting the Covenant Separatists, led by the Sangheili and their Unggoy and Lekgolo supporters. Fronts of this war include High Charity, Delta Halo, and areas of space where Covenant ships operate.
This is not necessarily the first internal dispute in the Covenant's society; when the current Arbiter was assigned to his office, he was reminded by the High Prophet of Mercy that an Arbiter was necessary during the Grunt Rebellion, a conflict between the Covenant and its lowest caste, the Unggoy.
How the faction comes to life
The High Prophet of Regret led a botched mission to Earth and was forced into The First Battle of Earth upon discovering what turns out to be the UNSC home world. He escapes to Delta Halo but is killed by the Master Chief, which is considered a significant failure in the Elites' mission to protect the leading caste of the Covenant. The Master Chief was assigned on a mission to capture and later kill a member of that caste. The remaining Prophets, led by the High Prophet of Truth, use this opportunity to replace the Elites with Brutes as their guards. However, this move effectively shames and angers the Elites, who have grown accustomed to their comfortable position in the caste system, and they threaten to resign from the High Council.
Later, the Elite Councilors are assassinated by the Brutes at the behest of the Prophets; this purge, along with the understanding of what the Halos actually are meant to do, help divide the Covenant along the lines seen in the war. Instead of a Great Journey, the Gravemind's revelation regarding the super weapon contradicts the Covenant's belief system and is motivating at least the Arbiter in his eventual opposition to the Covenant as they try to activate Delta Halo later in the game.
The remaining species in the Covenant make up the Covenant Loyalists.
Military Forces: The Prophets and their supporters
Commanded by Truth, the Loyalists include Jiralhanae, Kig-Yar, Yanme'e, and a few Unggoy castes, along with loyal ships of various classes to their cause.