For those who don't know "the undiscovered country' refers to the famous 'to be, or not to be' speech in Hamlet. Travelling to the undiscovered country is dying. No surprise the Klingons love Shakespeare and claim him as their own.
Trek's full of Shakespeare references. IRC Shatner was Plummer/Chang's understudy for a Shakespeare play. Stewart is obviously a Shakespearian/RSC actor too, the character famously loves a bit of Shakespeare. Brooks/Sisko was a Shakespearean actor, so was Zimmerman. I think they've started including more references in Strange New Worlds.
Also explains the acting you sometimes see in Trek. Most of the big names all started out doing Shakespeare in theaters.