The Covenant Loyalists are a splinter cell of the originally more powerful Covenant Empire. It consists of all species still loyal to their leaders and to their religon. The species include the Unggoy (During Late Era), Kig-Yar, Mgalekgolo (During Late Era), Jiralhanae, Yanme'e and the San'Shyuum. The Jiralhanae replaced the Sangheili as the main military force and once scared into extinction, that the Unggoy and Lekgolo joined their side
The Covenant Loyalists were the second faction partciptating in the Covenant Civil War, but was destroyed when the High Prophet of Truth was killed at the hands of the Arbiter. It's splinter cell, Covenant Remnants still exists, but poses no threat.