The most obvious way in which justice is represented in Agamemnon is in the victory of Agamemnon's armies over Ilion.
I set to mark
When shall stream up the glow of signal-flame,
The bale-fire bright, and tell its Trojan tale-
Troy town is ta'en:
It was Paris of Troy who took Helen of Sparta from her husband Menelaus, a Greek along with Agamemnon and Achilles. Paris took her because they had been promised to each other by the goddess Aphrodite as a reward for his praise of Aphrodite's beauty. It can therefore be argued that justice was served when the Danaans (Greeks) won the ten-year Trojan War and Helen was returned to her husband Menelaus and their daughter Hermione.
The concept of justice in Agamemnon is a dubious one by our standards for each act of justice involves personal revenge, violence, and death as when Clytemnestra exacts justice by slaying Agamemnon. Clytemnestra seeks justice for Agamemnon's intentional sacrifice of their daughter Iphigenia to appease the goddess Artemis, whom he insulted. At the end of the tragedy, Clytemnestra cries out to the gods who spoke in the oracle governing "O'er all the race of [Agamemnon] Pleisthenes," saying, "I pray thee let thine anger cease!" She claims that by her deed of murder a curse is lifted:
The bloody lust and murderous,
The inborn frenzy of our house,
Is ended, by my deed!
Clytemnestra clearly believes her acts of murder are the administration of justice because, as the Chorus says:
The children of the curse abide within
These halls of high estate--
And none [could] wrench from off the home of sin
The clinging grasp of fate.