Interesting quote.  The quote means that tyranny and anarchy are always related.  This applies to the play in a few different ways.  First, it could easily apply to Brutus.  Remember, he only decides to help kill Caesar because he thinks Caesar is starting to become a tyrant.  He believes he is saving Rome from anarchy because he believes when the conspirators seize control they will rule honestly and fairly, thereby, saving Rome from the tyranny of a corrupt Caesar and from the anarchy that would inevitably arise to topple him.  Second, it applies to the fact that Caesar is killed because the conspirators think he might become a tyrant.  Out of their decision to kill him arises anarchy as the conspirators decide who should seize control with Cassuis wanting one thing and Brutus wanting another.  Third, it applies to Cassuis, who longs after the power that Caesar had and who would himself become a tyrant, is instrumental in tricking Brutus to join the plot kill Caesar and throwing Rome into anarchy.  You could also analyze Antony's funeral speech and how he makes the conspirators seem like tyrants to the citizens of Rome and works them up so that they bring anarchy down upon Rome.