Derek Jacobi did not receive an Oscar nomination for portraying Claudius in Hamlet.
Derek Jacobi is actually one of the connective tissues between Laurence Olivier and Kenneth Branagh as before appearing in Branagh first directorial effort Henry V Jacobi starred along with Olivier in the filmed version of Othello. Anyway Jacobi is another master of the language in league with Olivier and Branagh. No doubt his mastery contributed to Branagh's casting of Jacobi as the chorus in Henry V. Branagh proceeded to cast him once again this time as Claudius. Jacobi's success with this role can be witnessed from one of the earliest scenes of the film where he is presenting his new wife to his people. Jacobi presents a different Claudius in this scene that is usually seen. Jacobi presents Claudius as a man truly enjoying his position power as well as marriage, but he actually suggests a real command of a King.
Throughout the film, with help from the complete version of the play, Jacobi is very effective by showing Claudius's own transformation as Hamlet's behavior becomes more suspicious. When Hamlet's madness seems to have no rhyme or reason to anyone other than Hamlet himself, Jacobi rather merely treating Hamlet like some sort of nuisance is far more effective by portraying an actual concern for his nephew. There certainly are most definitely traces of his concern for his own health, but Jacobi brings a greater depth of feeling with his work. There is the suggestion in his performance that he actually does to a certain extent care about his nephew's mental health. Jacobi never wastes his reactions in any of his scenes given a fuller portrait of Claudius mentally processing what Hamlet is doing.
Claudius changes his response to Hamlet one Hamlet organizes his mousetrap which is to use players to basically show a reenactment of the King's murder to get a response out of Claudius to show his guilt. Jacobi brilliantly handles Claudius's reaction making it a strong emotional response but he does not go too far. He makes it noticeable without a doubt, but it's far more powerful because Jacobi doesn't make it excessive. Jacobi even greater scene comes instantly afterwards when Claudius quickly goes to a confessional to try to plead forgiveness to God. Jacobi actually succeeds in stealing these scenes from Branagh, and that's not because Branagh is slouching in his role in anyway. Jacobi brings such a genuine poignancy as he shows the palatable guilt in Claudius, guilt worthy of a man who has murdered his own brother.
Claudius's reveal though also causes Hamlet to become rather sloppy in his plan, and it becomes obvious that Hamlet knows Claudius's crime. Jacobi adjusts his performance magnificently as Claudius becomes an active villain who is trying to plot the demise of his nephew. Unlike the other Claudius's who seem woefully inept, Jacobi manages to make the King an imposing figure. As I said earlier he actually carries a command with his performance to suggest his role as the King, and he transfers this command to Claudius as he tries to deal with the threat to his power, Hamlet. Jacobi is very effective by suggesting a greater intelligence in Claudius as he slowly tries to reason out what exactly to do with his problem. Jacobi brings a strong menace with his portrayal, particularly in the scenes where he believes he is organizing Hamlet's death, as he reveals the side of Claudius that slew his own brother.
Jacobi is terrific because he never allows himself to be forgotten behind Branagh's Hamlet, he always keeps Claudius as notable presence in every scene he is in, even the final duel which is one of the great highlights of Branagh's performance. Jacobi is great in the scene playing the deviousness of Claudius well behind his apparent jovial face who just wants to praise his nephew. Jacobi infuses the right deviousness in the scene as Claudius attempts to rid himself of his problem. Jacobi's best moment in the scene comes when his wife Gertrude decides to drink from the cup that Claudius purposefully poisoned for Hamlet. Jacobi is fantastic in the moment because it is not just an oh well moments, but Jacobi portrays Claudius as honestly heartbroken that his scheme has killed his wife who he did indeed love.
Derek Jacobi gives a great performance here as Claudius because he never let's the character fall into obscurity in the film, as Claudius very easily could have simply been forgotten behind the flamboyance of the titular character. He realizes the various facets of the role in a wonderful fashion as he never makes Claudius just the King, or just the villain, or just a guilt ridden man. Jacobi makes him all of those things into a believable whole, and by showing these different sides he makes Claudius a far more compelling character than he usually is. Jacobi makes a remarkable impact on the whole of the film refusing to ever be forgotten because he isn't the title character. Add to all that Jacobi incredible understanding and delivery of the language you have one of the best Shakespearean performances on film.