The ship, which was considered holy, belonged to T'Kuvma's father. Upon his death, when T'Kuvma was a child, it lay abandoned for children to play in until T'Kuvma rediscovered it and vowed to restore the honor of his House.
In 2256, the Sarcophagus was encountered by the USS Shenzhou at the edge of Federation space, six light years from Gamma Hydra. The vessel later instigated the Battle of the Binary Stars by firing on the Shenzhou, but was disabled by a bomb afterward and T'Kuvma was killed by a Starfleet boarding party. (DIS: "The Vulcan Hello", "Battle at the Binary Stars")
The vessel was left stranded in the binary system for six months afterwards, with dwindling food supplies and no way to repair or replace its dilithium processing unit. Kol of the House of Kor eventually arrived and bought the allegiance of the Sarcophagus's crew by bribing them with food, before claiming the vessel as his own and leaving Voq to die on the derelict Shenzhou. (DIS: "The Butcher's Knife Cares Not for the Lamb's Cry")
Kol used the Sarcophagus as his personal flagship, directing the war effort from its bridge. When an invitation was received from the planet Pahvo, Kol ordered the ship to set a course. (DIS: "Si Vis Pacem, Para Bellum")
Arriving at Pahvo in a cloaked state, Kol prepared to destroy the planet, but was forced to engage the USS Discovery when the Federation starship appeared in orbit. As Sarcophagus decloaked, Discovery used the ship's momentary vulnerability to beam a boarding party aboard. The Discovery then utilized its spore drive to outmaneuver the Klingon vessel, leading Kol to order Sarcophagus to recloak. However, this was exactly what the Starfleet ship wanted, as it enabled them to use sensors planted aboard to develop an algorithm to detect the imperfections in the Klingon cloaking technology. With the algorithm completed, Discovery was able to easily locate and destroy the Ship of the Dead. (DIS: "Into the Forest I Go")
Technical data Edit
The vessel was significantly larger than a Federation Walker-class starship, and was covered with thousands of hollow, ornamental, metallic pods that were tightly interlocked to form a symbolic armor. These caskets contained a "Black Fleet" of remains of warriors, dating back as far as thousands of years. T'Kuvma had also devised a way to emit a form of stealth mode described as a cloaking screen. The ship could generate a multitude of tractor beams from its "neck" section. It was armed with directed energy weapons and torpedoes, and possessed enough firepower to destroy the surface of a Class M planet.
Background information Edit
The viewscreen display of the vessel aboard USS Shenzhou identified this vessel as an "Unknown Klingon Command Vessel". The series' press kit identified it as "The Sarcophagus Ship", while other background sources identified it under the similarly titled "Klingon 'sarcophagus ship'".  
A feature on the ship in SFX magazine (issue 292, p. 83) described the ship as two hundred years old, and three times the size of its Federation counterparts. It was said to have no consoles, because its crew interfaced with their computers directly via their ornate silver masks.
In the Star Trek Online short story "Step Right Up", a disreputable Klingon archaeologist named Tortoth claimed to have recovered the ship's schematics from the wreckage of its final battle at Pahvo, and revealed a rebuilt Sarcophagus – equipped with modern (25th century) technology – at a press conference on Risa, where he invited viewers to place orders for a Sarcophagus of their own.  The blog post coincided the ship's release in the "Discovery Lock Box" in January 2018, designated as the "Sarcophagus Dreadnought Carrier". The Sarcophagus also appears in a "Task Force Operation" – a multi-player mission – that recreates the Battle of the Binary Stars.