Leonard "Bones" McCoy plays a less prominent role here than he did in previous Star Trek films, but he still proves to be an indispensable member of Enterprise's crew.
McCoy's big moment in The Undiscovered Country is his attempt to save Gorkon's life. Despite not knowing jack about Klingon anatomy, McCoy mounts a desperate effort to save the Chancellor's life. Even though he ultimately fails, we'd argue that his actions go a long way toward showing Azetbur that Kirk and McCoy are good men.
Of course, McCoy is still thrown into a Klingon "gulag" with Kirk. (And unlike Kirk, he doesn't even get to make out with a shapeshifter. Lame.) Regardless, McCoy's unerring commitment to the Hippocratic Oath is refreshing in a movie filled with prejudice and distrust.