In a way, Star Trek VI: The Undiscovered Country featured three different kinds of appearances by Odo from Star Trek: Deep Space Nine. Though the actual character of Constable Odo, who wouldn't even debut until 1993 - two years after Star Trek VI arrived in movie theaters - wasn't in the movie, The Undiscovered Country featured a different kind of shapeshifter and the Director's Cut of the film included a cameo by the late Rene Auberjonois, who played Odo for seven seasons on DS9.
The sixth and final film starring the cast of The Original Series, Star Trek VI: The Undiscovered Country was about the end of the Cold War between the Klingon Empire and the United Federation of Planets. But while Captain James T. Kirk (William Shatner) and the Starship Enterprise-A were negotiating galactic peace with the Klingon High Chancellor Gorkon (David Warner), a conspiracy between Starfleet, Romulans and Klingon dissidents framed Kirk and Dr. Leonard McCoy (DeForrest Kelley) for Gorkon's assassination. It was up to Spock (Leonard Nimoy) to prove Kirk's innocence and rescue him from imprisonment. The Enterprise crew then uncovered the conspirators and saved the life of the new Chancellor, Gorkon's daughter Azetbur (Rosanna DeSoto), ensuring the peace between the Federation and the Klingons, which would last into the era of Star Trek: The Next Generation over 70 years later.
However, the extended Director's Cut of Star Trek VI that was released on DVD, Laserdisc, and VHS featured a cameo by Colonel West, played by Rene Auberjonois. West was a Starfleet Officer who presented Operation Retrieve, a plan to rescue Kirk and McCoy from the Klingons, which was not approved by the Federation President (Kurtwood Smith). When the president feared that such a rescue attempt could ignite a full-scale war, West memorably boasted, "Then quite frankly, Mr. President, we can clean their chronometers." At the conclusion of the Star Trek VI Director's Cut, the Klingon who tried to assassinate Azetbur at the Khitomer Peace Conference was revealed to be West incognito; the traitorous Colonel was actually one of the conspirators and he was killed and exposed by Montgomery Scott (James Doohan).
Auberjonois isn't in the credits for Star Trek VI, not even in the Director's Cut where his character appears, and the actor was surprised to learn his scenes were restored in the extended version. However, after 2009, only the theatrical cut of Star Trek VI without West is available for purchase, although Colonel West's scenes can be seen on YouTube. As for how Auberjonois was cast in the film, the talented actor happened to be longtime friends of director Nicholas Meyer, who invited him to play the role of the Starfleet traitor. And once Auberjonois was part of the Star Trek family, he was soon cast as Constable Odo in Star Trek: Deep Space Nine.
Meanwhile, a predecessor to Odo appears in Star Trek VI: At the Klingon penal planet Rura Penthe, Kirk and McCoy encounter Martia, a Chameloid played by Iman. As a shapeshifter, Martia took on several forms, including aliens and Captain Kirk himself. Martia predated the Founders, Odo's race of liquid-based changelings from the Gamma Quadrant who founded the Dominion and became the main villains of DS9. However, Martia is the only known Chameloid in Star Trek canon and it was never clarified nor retconned whether Martia was also a Founder or whether Chameloids just happen to be an entirely separate race of shapeshifters. In the film, Martia was memorably killed by the Klingons after she took Kirk's form and brawled with the Captain (after she kissed him and teased that Kirk kissing himself "must have been your lifelong ambition").
Fascinatingly, Star Trek VI's Odo connection continues with actor Kurtwood Smith. After playing the Federation President, Smith was cast in DS9 as Thrax, Odo's predecessor as Chief of Security when the space station was still under Cardassian control and called Terok Nor. In the DS9 season 5 episode, "Things Past", when Captain Benjamin Sisko (Avery Brooks) and his crew found themselves inhabiting Bajorian bodies in Odo's memory of Terok Nor, it turned out Thrax was actually the younger version of Odo himself. Indeed, Star Trek VI intriguingly contains several elements of Constable Odo that would one day coalesce into Deep Space Nine's beloved shapeshifter.