Character Analysis
Sarek is Spock's father and the Vulcan ambassador to the Federation. His role in the story is to present Kirk with his father's lightsaber and help him get off Tatooine, so the aging admiral can fulfill his destiny and become a Jedi.
Wait…
Sorry, we got Sarek confused with Obi-Wan Kenobi again. It's all those dramatic entrances with the removing of the hood to reveal the face. Throws us every time.
Also, there's the fact that both Sarek and Obi-Wan act as the mentor characters in their respective science fiction adventures. Just like Obi-Wan informs Luke about the Jedi order, Sarek teaches Kirk about Vulcan culture and the katra.
And he slips into this role right away:
SAREK: Only his body was in death, Kirk, and you were the last one to be with him.
KIRK: Yes, I was.
SAREK: And you must know that you should have come with him to Vulcan.
KIRK: But why?
SAREK: Because he asked you to. He entrusted you with his very essence, with everything that was not of the body. He asked you to bring him to us and to bring that which he gave you, his katra, his living spirit.
KIRK: Sir, your son meant more to me that you can know. I'd have given my life if it would have saved his. Believe me when I tell you, he made no request of me.
SAREK: He would not have spoken of it openly.
KIRK: Then how—?
There's a lot of dialogue there, but notice how the back-and-forth between Kirk and Sarek is exactly like a student and teacher. Sarek provides Kirk with information—and incidentally provides said information to the audience in a little thing we like to call exposition. Kirk asks a question or provides a statement that prompts Sarek to provide even more lessons.
And so it goes until Kirk has the information he needs to start his question.
Once they discover that Spock's katra has been locked away inside McCoy's noggin, Sarek performs the second role of the mentor: he sends the hero on the quest.
Just like Obi-Wan telling Luke he must come with him to Alderaan, Sarek tells Kirk what he needs to get done:
SAREK: You must bring them to Mount Seleya on Vulcan. Only there can both find peace.
Then he disappears until the end of the story, when he appears on Vulcan to request the refusion. During the interim, we suppose he does whatever it is mentors do while the hero fulfills his quest. (Just hanging out in the mentor's lounge or something?)