The Undiscovered Country's story is all about military intrigue, so it's only right that it features an appropriately intense score.
Although the composer, Cliff Eidelman, scored his first feature film in 1989 with Magdalene, The Undiscovered Country was his first real shot at the big leagues. The dude was only twenty-six years old.
Of course, the classics are all here. We have several variations on the main Star Trek theme, though it's used perhaps less prominently than in previous entries in the series.
The score is most similar to that of The Wrath of Khan—which makes sense, given that both were directed by Nicholas Meyer. But that's not the only similarity. Both films lean toward the "military" side of Star Trek, and consequently they feature scores that set a martial tone.
For example, the film's overture might sound like a death metal song if you recorded it with electric guitars. Likewise, "The Final Battle for Peace" provides an aural interpretation of Enterprise's final battle with Chang. On the other side of the fence, we have tense tracks like "Assassination" which mirrors the plot's slow-burning political intrigue.
In other words, this is not music to chillax to. If you want that, stick with your Jack Johnson, folks.