“At the end of seven years, at the time (במועד) of the Shemittah year, during the Sukkos festival, when all of the Jewish people come to appear before Hashem.”
he Gemara explains why each of these terms is necessary. If the Torah would have just said במועד (which can mean on the Festival), we may have thought that this means on Rosh Hashana. Therefore the Pasuk has to specify “during the Sukkos festival”.
Tosfos questions that once the Torah writes “when all of the Jewish people come to appear before Hashem”, we would know that it cannot mean Rosh Hashanah, since it isn’t one of the pilgrimage festivals. So why then is it necessary to state “during the Sukkos festival”?
Tosfos explains that we would of otherwise thought that the Mitzvah of Hakhel should take place on Pesach, which is one of the pilgrimage festivals. Therefore, the Torah must qualify that it means Sukkos.
From the fact that we would have initially thought that Hakhel should take place on Pesach, we see that there is a strong connection between the idea of Hakhel and the Yomtov of Pesach.