What is the significance of the following passage:"We will establish our estate upon Our eldest, Malcolm, whom we name hereafter The Prince of Cumberland."
As was mentioned in the previous post, King Duncan makes this comment in Act One, Scene Four, in which he names Malcolm heir to his throne. This is significant because the Three Witches had told Macbeth that he would become king one day. Macbeth now realizes that in order for him to become king, he will need to get rid of Malcolm. Macbeth's ambition is spurred as he comes to terms with what he will have to do in order to become king. After Malcolm is named prince, Macbeth says to himself,
The prince of Cumberland! That is a step on which I must fall down, or else o'erleap, for in my way it lies. Stars, hide your fires; Let not light see my black and deep desires (1.4.50-53).
Macbeth is essentially saying that Malcolm is in his way, but he is willing to take the necessary steps to reach his desired position as king. As the play develops, Macbeth commits regicide, but Malcolm is able to flee the country. Macbeth becomes haunted and preoccupied with the possibility that Malcolm might return back to Scotland to take the crown from his head. Malcolm eventually ends up gaining enough support to overthrow Macbeth as king by the end of the play.
In these lines, King Duncan is naming his oldest son, Malcolm, to be the next king of Scotland. The only problem is that Macbeth has been promised the kingship by the witches in the first scene of the play. Part of the witches' prediction has already come true. Duncan has just named Macbeth as Thane of Cawdor. In his haste to be king, Macbeth thinks that Duncan may also name him his heir. Instead, Duncan chooses Malcolm for that honor. This choice provides the entire motivation for the rest of the play. As Macbeth says,
"The Prince of Cumberland! That is a step
On which I must fall down, or else o'erleap,
For in my way it lies." (I, iv, 55-57)
In other words, since Malcolm has been named heir to the throne, Macbeth must figure out a way to get Malcolm out of the way so that Macbeth can be king, as the witches have foretold.