Re-accepting the old Torah prepares for the new

הלימוד בליל שבועות עפ"י אומרם ז"ל אם שמוע בישן תשמע בחדש.

The learning done on the night of Shavuos is based on what Chazal said: "If you will surely listen" — if you listen to the old, you will merit to hear the new.

The Sefas Emes explains the custom of learning Torah through the night of Shavuos. Chazal expound the doubled language "im shamoa tishma" to mean that one who holds onto the Torah already received ("the old") becomes a vessel to receive the new light of Torah that descends anew each Shavuos.

לכן צריכין לקבל בלילה זו התורה שלמדנו עד עתה.

Therefore on this night we must re-accept the Torah that we have learned until now.

Before one can take in the fresh revelation of Shavuos, one must first re-receive and reaffirm everything already learned. The "old" Torah is not discarded; it is gathered up and rededicated.

וזה הכנה להחדש:

And this is the preparation for the new.

Reaffirming the Torah one already possesses is precisely the hachanah (preparation) that opens a person to receive the new chiddushim (fresh insights) and renewed kabbalas haTorah of Shavuos.

Summary: The all-night learning of Shavuos works by "listening to the old" — re-accepting the Torah already learned — which is the very preparation that makes one a vessel to receive the renewed light of Torah given afresh each Shavuos.