(covers information from several alternate timelines)
Sometime prior to the 2150s, future Tellarite ambassador Gral stood on the command deck of a Tellarite cruiser in Andorian space during a conflict where they were "driving those blue demons back into their territory." (ENT: "Babel One")
In 2154, one of these vessels was initially believed responsible for the destruction of the Andorian warship Kumari, though it was later found to be a Romulan drone ship in disguise. (ENT: "Babel One")
Several Tellarite cruisers, along with Andorian and Vulcan ships, later formed a fleet to track down and destroy the Romulan vessel.
In the mirror universe, the Tellarite rebels utilized this class of vessel, which were among those attacking the ISS Avenger at the Terran fleet rendezvous point. (ENT: "In a Mirror, Darkly, Part II")
Tellarite cruisers were armed with particle cannons, which left a signature unique to Tellarite technology. They were said to be inferior in design to the Andorian battle cruisers of the era, with Gral noting that a single Tellarite cruiser would not stand a chance against two Andorian equivalents. (ENT: "Babel One")
Ships of the class
According to the novel A Choice of Futures Tellarites bought their ships from external sources in this time.
Star Trek: Fleet Command features two Tellarite cruisers by the names Kehra and Phindra.