Arguably, there is situational irony in Caesar's murder at the Capitol.
With situational irony, the expected outcome of an event doesn't occur—instead, something happens that is the opposite of what we might have predicted. It would seem, therefore, that what happens later to Caesar "in relation to the preceding events" is ironic because when Julius Caesar returns to Rome after the death of Pompey on the feast of Lupercal in Act I, he is initially received with great adulation and enthusiasm, so his death would not be expected later on. In short, the parades in Caesar's honor are situationally ironic; the love of the people, which usually helps someone stay in power, here causes the conspirators to murder Caesar.
Cassius begs Caesar to restore Publius Cimber to citizenship, but Caesar refuses,
I could be well moved if I were as you.
If I could pray to move, prayers would move me.
But I am constant as the northern star.... (3.1.63-65)
Soon after this refusal, Caesar is slain, a condition which lends irony to his words about being "constant as the northern star."