Multiple realities
(covers information from several alternate timelines)

Klingon cruiser was a ship designation, which referred to several different Klingon ship types in the 23rd century and 24th century.

In the Kobayashi Maru scenario in 2285, the K't'inga-class was identified as a Klingon cruiser. (Star Trek II: The Wrath of Khan)

In 2364, the Klingon cruiser IKS T'Acog was sent to apprehend the Klingon criminals Korris, Konmel, and Kunivas, who had commandeered the Talarian freighter Batris. The T'Acog attempted to disable the Talarian ship with phasers and photon torpedoes. The Batris was however able to destroy the T'Acog in the battle. The debris of the ship was discovered by the USS Enterprise-D, though it couldn't be determined at first from the debris if the cruiser had been a Klingon or a Romulan vessel. The second Klingon ship sent, commanded by K'Nera, was also a Klingon cruiser. (TNG: "Heart of Glory")

The following year, another Klingon cruiser passing near the Theta 116 solar system reported discovering pieces of a strange vessel in the upper atmosphere of the planet Theta VIII. In response, the Enterprise-D diverted from its course to investigate. (TNG: "The Royale")

The IKS Pagh, a Klingon Bird-of-Prey, and the IKS P'Rang were referred to as Klingon cruisers in 2365. (TNG: "A Matter Of Honor", "The Emissary")

In 2370, Julian Bashir called a mirror universe Vor'cha-class ship a Klingon cruiser. (DS9: "Crossover")

Three different starship classes were designated Klingon cruiser. It is unknown whether the references in "Heart of Glory", "The Royale" and "The Emissary" referred to one of those three or to yet another class.