In summary:

Mordecai, a Jew, would not condone idolatry, and showed his loyalty to God by not bowing to Haman, the official who was second-in-command to the king. Haman hated Mordecai and plotted to kill all the Jews in Persia. Mordecai encouraged his cousin, Queen Esther, to go to the king and save her people. She did so and the plot turned against Haman, who ironically was hanged on the same gallows he had prepared for Mordecai.

Haman was succeeded by Mordecai, who now was second-in-command to the king. He encouraged his people to defend themselves against the scheduled massacre planned by Haman. Persian officials also assisted in protecting the Jews, an event celebrated by the annual Feast of Purim (Esther 9:26-32)
In some detail

Mordecai was the hero in the Book of Esther. He was a resident of Susa (Shushan), the Persian capitol during the reign of Ahasuerus (Xerxes 1). When Mordecai’s uncle, Abihail, died (Esther 2:5), Mordecai took his orphaned cousin, Esther, into his home as her adoptive father. After Esther became Ahasuerus’ queen, Mordecai discovered a plot to assassinate King Ahasuerus, and exposed it, saving the king’s life (Esther 2:21-22).

The story of Esther usually focuses on Esther the Jewess who  became queen and eventually saved her people from destruction,
Esther means star. But there was another  ‘star in the Book of Esther.
Mordecai was an intelligent loving, stainchly loyal, courageous man, willing to risk his life for God for His people.. In terms of “leadership styles”, He was an excellent example of servant-leadership. There is no evidence in Scripture that Mordecai was married, so when he adopted his uncle’s orphaned daughter, Hadassah, Mordecai  played the part of a single father.
Hadassah, who was given the Babylonian name of Esther, was taken with other beautiful young virgins to the king’s palace to replace the deposed Queen Vashti. Mordecai had taught Hadassah to be self-confident and sophisticated. Though he may not have been surprised that Esther was chosen to be Queen, Mordecai  knew that God was present and moving in the situation for His purpose, and he wisely instructed his cousin to keep quiet about her origins, and certainly not tell  the king.
Mordecai held some  office in the king’s court, which is why he could sit at the gates. After Esther was chosen as queen, he overheard ad exposed a plot to assassinate the king. The conspirators were hanged and Queen Esther saw to it that Mordecai’s actions were recorded in the king’s chronicles, although no reward was immediately offered.
But there was evil brewing in the shadows of the king’s courts. Haman the Agagite had been appointed to the highest position in the kingdom and demanded that everyone bow before him. Mordecai refused to comply. Haman was outraged and devised a plan to destroy not only Mordecai, but all the Jews in the empire. The king gave Haman the authority to execute his plan, beiing unaware of the nationality of his beloved queen. Haman had letters sent to every governor of every province that on a certain day they would coordinate the total annihilation of every Judean man, woman and child.
Mordecai learned of this deadly plan. Seating himself before the king’s gate, he wore sackcloth and ashes, wailing loudly. His reaction caught Esther’s attention and through a messenger asked the reason for his grief. The messenger brought back news from Mordecai of Haman’s deadly conspiracy. Together they agreed that Esther should take the opportunity to reveal the plot to the king.  In response, she requested that a banquet be held for only Haman and the king.
That night, the king could not sleep. To pass the night, he asked for the chronicles to read, and there he discovered Mordecai’s exposure of the assassination attempt, and that he had never been honored. The next morning the king asked Haman, What shall be done for the man whom the king delights to honor? Thinking the king was referring to him, the conceited Haman pompously suggested that such a man should be given a robe of the king, have a royal crest placed on his head and be paraded through the city on one of the king’s horses, escorted by one of the king’s top men, proclaiming, “Thus shall it be done to the man whom the king delights to honor!” Much to Haman’s shock, the king told Haman to do all he had suggested for Mordecai!
Haman had no option but to obey, and after he had paraded Mordecai as he had described, went home humiliated. That night, at the banquet that Queen Esther had arranged, the king asked Esther what her special request was, offering up to half of his kingdom. Esther then revealed the wicked plan to exterminate her people, revealing that she was Jewish, and exposed Haman as the perpetrator.
Haman was hanged on the gallows he had built for Mordecai. Esther revealed to the king Mordecai’s relationship to her and the king promoted him to Haman’s position, giving him all of Haman’s property. Mordecai used this opportunity to send out letters in the king’s name that all Judeans were to unite, to arm and defend themselves against any that would assault them. The letters were distributed and the plan to destroy God’s people was turned on its head. Mordecai’s powerful position gave God’s people the boldness and confidence to defend themselves.
Mordecai’s excellence was recorded in the chronicles of the kings of Media and Persia. He was a man of commitment and courage, who walked with wisdom and sensitivity to God. He had tremendous love for Esther and all of God’s people. Mordecai stood up to his adversary, risking his own life for the collective lives of his people, and earned a name and a reputation worthy of respect among God’s people for all time.
Esther 10:3  For Mordecai the Jew was next unto king Ahasuerus, and great among the Jews, and accepted of the multitude of his brethren, seeking the wealth of his people, and speaking peace to all his seed.
This video shows an Israeli rabbi visiting the graves of Mordecai and Esther … in Iran! Apparently the graves are well preserved and visited by Jews, Christians and even Muslims.
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