He inherited Haman’s position and house and became a renowned public figure. But the sages say that he did not remain in Shushan. He moved to Jerusalem and became a Temple official. This may have been for positive reasons because he had a great love for the Holy Land and had actually lived there before the Persian episode.
Alternatively, his departure may have been because of enemies still lurking in Persia who were determined to bring him down and kill him.
Another possibility is that he had originally been married to Esther before she became the king’s wife, and now that she had saved the day for the Jews, Mordechai felt his presence would embarrass her.
It is also possible that since the end of the M’gillah implies (according to Rashi) that some of his Jewish brethren were critical of him, he felt safer being away from them.
(This D’var Torah is partly based on an article by Rabbi J. Simcha Cohen of the USA.)