in the two stories, Claudius andMacbeth, are shamed for killing the respective "good kings" from their stories. In particular, the good king Duncan may have been representative of James I, whose peaceful ascension to power would prevent such tragedies as occurred in the Shakespearean plays from happening. In this way, Shakespeare did indeed work with the power structures of his time to create art and expression.

In contrast, the influence of Hamlet has been thought by New Historicists to represent a far more subversive sentiment. Hamlet was written during the reign of Elizabeth I, and one does not have to look far to find a weak, uncertain, and irresponsible matriarch in the play. Gertrude seems to be representative of Elizabeth in her old age: Elizabeth had refused to name an heir, creating great national turmoil. Shakespeare may have written the play in part to show Elizabeth I's ineptitude in her old age and what can come of an irresponsible and neglectful queen. The degree to which this may be rooted in misogyny on the part of Shakespeare is hotly and frequently debated, and the idea that he may have favored a patriarchy is an object of contention.

To answer your question, it is important to review what New Historicism is. The New World Encyclopedia defines the concept:

New Historicism is an approach to literary criticism and literary theory based on the premise that a literary work should be considered a product of the time, place, and historical circumstances of its composition rather than as an isolated work of art or text.

In other words, this approach tries to understand a piece of literature based not only by what is within it, but also on the context of the historical time period in which it was written.

With this in mind, New Historicism can be applied to both of Shakespeare's plays, Macbeth and Hamlet.

Shakespeare wrote his plays for an Elizabethan/Jacobean audience. This era was known as the English Renaissance, influenced by the Italian Renaissance that began a hundred years prior. After the political upheavals that had dealt such heavy blows to her country prior to her ascension to the throne, Elizabeth I welcomed and supported the rebirth of the arts. When she died, James I continued the practice.

Attending the theater was, surprisingly, something that appealed to all socioeconomic levels of society. The "cheap" seats, ironically, were the closest seats. What we perceive as the "nose bleed" section today was reserved for royalty, to rise above the more common folk. (It was so popular that when the plague broke out, the theater was the first place to be closed.)

In terms of New Historicism, it would be important to know the historical context of the play's audience. The audience knew its history and would recognize historical figures portrayed. Things we don't find funny today would have been openly comic then.

A playwright who was a wise man would make sure to direct some part of his play to compliment the current monarch. In Macbeth, the man who takes over when the tyrant Macbeth is killed is Malcolm, who is presented as a truly virtuous man and was related to James I (Shakespeare's king), who was also James VI of Scotland (the setting of the play).

In both Macbeth and Hamlet, it is important to note that Elizabethans believed whole-heartedly in the supernatural. Witches and apparitions in Macbeth, and the Ghost in Hamlet would have captivated the audience. Whereas we might think these aspects of the play silly, Shakespeare's audiences would have watched while holding a collective breath. (Witch-hunts were real!)

Also during this time period, the practice of hospitality was a very serious affair. If someone was in your home, whether a friend or archenemy, his safety was guaranteed. It was a question of honor. So in Macbeth, not only was Macbeth killing his king, but also his guest.

Elizabethans believed that kings and queens were chosen by God. Therefore, it was a mortal sin to kill a king. Macbeth does just that, upsetting the balance of the universe which is restored with his death and the rightful king on the throne. Hamlet's struggle as to whether to kill Claudius is based on this and the supernatural. If the Ghost is an evil apparition, he could lose his soul to eternal damnation by killing Claudius, if his uncle did not kill Old Hamlet. But if Claudius did, Hamlet is safe.

With these things in mind, in order to comprehend the implications and relevance of these plays, one needs to be aware of the historical context of when each was written.

Additional source:

http://www.enotes.com/hamlet/historical-background

http://www.enotes.com/topics/black-death

New historicism is a kind of literary criticism that arose in the 1980s.  One of the ways in which it differs from traditional historicism is in its emphasis on a multiplicity of historical contexts for literary works, rather than single contexts.  For instance, E. M. W. Tillyard’s famous book The Elizabethan World Picture can be seen as a product of traditional historical criticism. The very title of the book suggests that there was such a thing as “The” Elizabethan world picture. In other words, the very title of the book implies that Elizabethans broadly agreed about how to view the world. New historicists would argue, on the other hand, that it is too simplistic to talk about any single, unified view of the world during any historical era, especially the Elizabethan period, which was a time of enormous tension (especially having to do with religion). Instead, new historicists would suggest that any historical era, event, or product is a site of conflict and contention and negotiation. In other words, new historicism often emphasizes power struggles of all kinds in every aspect of history, including literary texts.

Power struggles, of course, are main features of Hamlet, Macbeth, and Othello. In Hamlet, for example, Hamlet becomes engaged in a highly dangerous power struggle with his uncle, Claudius. In Macbeth, the title character struggles for power not only with other Scottish aristocrats but also with his own wife. In Othello, Iago is engaged in a struggle for power with Othello, with Cassio, and even with Desdemona, although none of these three characters is really aware of the struggle until the end of the play. A new historicist analysis of the power struggles in these plays would, however, not stop with these obvious struggles but would explore the ways in which issues of power are all-pervasive in these dramas. New historicists would also explore the ways in which these plays were not only influenced by history (a common approach of traditional historicism) but how they also in turn participated in history and influenced history themselves.

See: E. M. W. Tillyard, The Elizabethan World Picture (London: Chatto and Windus, 1943).

See also: H. Aram Veeser, ed. The New Historicism (New York: Routledge, 1989).