Aharon's teshuvah and the Clouds of Glory

איתא ענני כבוד בזכות אהרן.

It is brought down that the Clouds of Glory (ananei kavod) were in the merit of Aharon.

Chazal teach that of the three gifts Bnei Yisrael received in the midbar — the mann, the well, and the protective Clouds of Glory — the Clouds came specifically through the zechus (merit) of Aharon HaKohen.

ולפי שאהרן הי' בעל תשובה והכניס עצמו בחטא ישראל והשיב אח"כ כולם בתשובה.

And since Aharon was a baal teshuvah, who entered into the sin of Yisrael and afterward brought them all back in teshuvah.

At the cheit ha'egel Aharon allowed himself to become bound up with the sin of the people, not to join it but to absorb it, and through that very closeness he was later able to lead all of Klal Yisrael back to Hashem in teshuvah.

לכן מתנה שלו נשאר לדורות שאחר עשי"ת מתגלה הארת ענני כבוד בסוכות:

Therefore his gift remains for all generations, that after the Aseres Yemei Teshuvah (Ten Days of Repentance) the light of the Clouds of Glory is revealed on Sukkos.

Because Aharon's avodah was the avodah of teshuvah, his gift fits precisely the season that follows Rosh Hashanah and Yom Kippur: once we have done teshuvah, the same sheltering light of the Clouds is revealed anew in the sukkah every year.

Summary: The Clouds of Glory came through Aharon, the baal teshuvah who absorbed Yisrael's sin and then returned them to Hashem; therefore his gift shines specifically on Sukkos, which follows the days of teshuvah, when the light of those Clouds is revealed once again in the sukkah.