The Gemara teaches that nonetheless, they reaccepted the Torah in the days of Achashveirosh. This acceptance was done wilfully of their own volition.
That being the case, Purim is connected to Matan Torah and by ex-tension to Hakhel. The Rambam teaches that the gathering of Hakhel was a recreation and reexperiencing of Matan Torah.
The Megillah also emphasises the idea of unity and gathering of the Jewish people, which is another theme of Hakhel.
Before she would approach the king, Esther asked Mordechai to go and gather the Jewish people together לך כנוס את כל היהודים . Esther understood that the unity of the Jews would stand in her merit.
Similarly in the decree that gave the Jews permission to fight back against their enemies, Mordechai wrote להקהל ולעמוד על נפשם that they should gather (הקהל) and stand up for their lives.