The Klingons gave the Romulans some older warships with dilithium warp cores. Why do Romulan Warbirds use quantum singularities instead?
It is speculated outside of canon that the Klingons and Romulans enjoyed a brief and tumultuous alliance during the mid-23rd century, during which time the Klingons traded their more rugged D7-Class Battlecruiser (either the blueprints, actual hulls, or both) for Romulan cloaking technology. This idea comes from the Original Series episode "The Enterprise Incident", in which Romulans are seen using ships of Klingon design.
The existence of a "Romulan-Klingon alliance" in the 23rd century has never been explicitly stated. In "The Enterprise Incident", all that was said was that "Intelligence reports Romulans now using Klingon design." The Making of Star Trek (finished during the early part of the third season of TOS) does say, however, that the intention at the time was to have the Klingons and Romulans form an alliance against the Federation. (Memory Alpha/Romulan-Klingon Relations)
This idea was explored in more detail in the expanded universe. You can get more info about it at Memory Beta/Klingon-Romulan Alliance. The most canon reference to this alliance seems to be in the TNG Technical Manual.
According to the Star Trek: The Next Generation Technical Journal, the Romulan cloaking device was acquired by the Klingons as an exchange for several D7-class battle cruisers for the Romulans during the Alliance. (Memory Beta/Klingon-Romulan Alliance)
The Romulan D'Deridex-Class warbird was revealed to be powered using a forced quantum singularity in TNG: "Face of the Enemy", but this class of ship did not seem to exist until the mid 24th-century, well after this alliance.