Final answer:
The passage in question pertains to Shakespeare's play 'Hamlet,' and it reflects on the emotional challenges and themes as discussed in T.S. Eliot's critical essay 'Hamlet and His Problems.'
Step-by-step explanation:
The context of the passage "Something he left imperfect in the state, which since his coming forth is thought of, which imports to the kingdom so much fear and danger that his personal return was most requir'd and necessary" is from the play Hamlet by William Shakespeare. The quoted material touches upon the themes that T.S. Eliot discusses in his essay 'Hamlet and His Problems,' where he critiques the play and the character of Hamlet, examining the inability of the protagonist to express his overwhelming emotions, which Shakespeare could not adequately convey through the plot or other characters. Eliot suggests that the play is Shakespeare's attempt to express Hamlet's inner turmoil in reaction to his mother's actions and the inadequacy of her character to evoke the appropriate emotional response from him, leading to a greater sense of Hamlet's dissatisfaction and indecision.