What plot did Mordecai uncover while sitting at the king's gate?

Answer: A plan to assassinate the king

Two eunuchs, Bigthan and Teresh, conspired to kill Xerxes; Mordecai told Esther, and it was recorded in the royal chronicles.

“In those days, while Mordecai was sitting at the king’s gate, Bigthan and Teresh, two of the king’s eunuchs who guarded the entrance, grew angry and conspired to assassinate King Xerxes.”— Esther 2:21 (BSB)