The Romulan-Klingon Alliance was an alliance between the Romulan Star Empire and the Klingon Empire during the 23rd century. Such an alliance was evidenced in 2267 when Romulans engaged the USS Enterprise using Klingon-designed D7-class battle cruisers. (TOS: "The Enterprise Incident").
The existence of this alliance 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. The only real indication in any series that an alliance was ever in effect is in "Reunion", where Riker says in response to a suggestion that the Klingons and Romulans were working together: "A new Klingon alliance with the Romulans?" By saying "new" it implies that there had been an "old" one at some point. The two powers were "blood enemies" for 75 years prior to the episode, so any former alliance would most likely have had to have ended prior to that. The Battle of Klach D'Kel Brakt in 2271, mentioned in the Star Trek: Deep Space Nine episode "Blood Oath", might have been at or near that end of the alliance, as it took place 96 years prior to the episode. However, since another 21 years would pass prior to being blood enemies, it is likely the alliance attempted to remain intact thereafter.
It is possible that the Romulans and Klingons had a second alliance as well. In "The Neutral Zone", Worf says the Romulans "killed my parents in an attack on Khitomer at a time when they were supposed to be our allies." That was 2346, and would require that the two races be both blood enemies and allied powers at the same time. This is possible as governments will often put aside philosophical or historical differences in favor of political expediency or gain, but it is highly speculative. However, in Star Trek VI: The Undiscovered Country, there are Romulan delegates present at the Khitomer Conference, so it is possible that some kind of relationship between the Klingons and the Romulans also extended from those events (even though Nanclus turned out to be one of the conspirators involved in the assassination of Gorkon and the Federation president).
According to the Star Trek: The Next Generation Technical Journal, the Romulan cloaking device was acquired by the Klingons as an exchange to several D7-class battle cruisers for the Romulans during the Alliance. In fact according to apocryphal accounts, in Seven Deadly Sins, Romulans required the power system of the D7-class ships to provide the power required to use the new improved cloaking device.