This is the quest that rewards you with the Exotic scout rifle "Touch of Malice" from "The Taken King" DLC. The requirements for getting to this quest are having completed the "King's Fall" raid at least once and having completed the quests "Shattered Past," "Hunger Pangs" pt. 1, "Hunger Pangs" pt.2, and "Hunger Pangs" pt. 3. These are started by acquiring the calcified fragment Grimoire pickups in "The Taken King." The requirements for total number of fragments needed per quest are 1, 15, 30, and 45.
This Planet Destiny guide over Touch of Malice, while fairly basic, is also straightforward and really good in my opinion.https://planetdestiny.com/touch-of-malice-quest-guide/
Also included is the relative location of all of the fragments in a video by YouTuber "Gaming Since Gaming."