In Shakespeare's Macbeth, once Macbeth has killed the king and been crowned himself, two new desires emerge.
First, Macbeth wants to be safe in his kingship. He is worried about rebellions against him. Banquo in particular is a threat since he knows the details of the witches' prophecies, and could suspect Macbeth (Banquo does suspect, but he doesn't reveal that to Macbeth). Macduff is also a possible threat, since he was the one who questioned Macbeth's killing of the grooms and did not attend Macbeth's coronation, which is a public slight.
Second, Macbeth's ambition has become such that being king himself is no longer enough. Once he is crowned, he begins plotting to create a dynasty, with Scotland being ruled by his heirs. This adds pressure and anxiety to Macbeth's life, and what he must do (kill Banquo and Fleance) to ensure his heirs will rule, adds risk.
Macbeth does have a desire to be "safely thus" once he becomes king, but he never achieves this desire.
Macbeth is such an ambitious character who can do anything to reach his goal. Macbeth's target is the removal of the hindrances to his way.
To become the king, at first, he kills King Duncan. Then, to make his path smoother and in order to secure his kingship, he keeps murdering on and on, because he believes: "To be thus is nothing,/ But to be safely thus." (Act 3, Scene 1). His inner gluttony and ambition lead him to fulfill the desire to hold on the throne at any cost. He knows that the way he has chosen is an evil way, he does not have the public support on his side. So, it is not enough for him to reach the throne, he must ensure the security of his power also. His "vaulting" ambition, along with the witches' and lady Macbeth's spurring instigation, makes him more paranoid.
As a new king, Macbeth plots to finish his foes to secure his throne and thus, he tries to ensure his safety.