Shavuot is in many ways the completion of the Pesach festival.
Its very name, Shavuot, or Weeks, attests to the connection between the two festivals, insofar as Shavuot is not connected to a specific day of the month.
It relates, in fact, to the counting of forty-nine days after Pesach.
And only when this seven weeks of the counting of the Omer is completed is Shavuot celebrated, on the fiftieth day.
The other name of the festival—Atzeret—is also indicative of this special connection.
It means a final festive day.
And just as the festival of Sukkot has its own atzeret on the eighth day (Shemini Atzeret), so does Pesach have its own.
However, the atzeret of Pesach does not fall immediately after the festival, as with Sukkot, but rather fifty days later—on the festival of Shavuot.
This link between the festivals of Pesach and Shavuot is not just formal and external: it is an expression of the intrinsic connection between them.
In other words, Pesach and Shavuot is not just formal and external—it is an expression of the intrinsic connection between them.
In other words, Pesach—the festival of redemption and freedom—is completed only on Shavuot, which is the festival of the giving the Torah.
Thus, Pesach without Shavuot is incomplete and lacking.
And in the same way, Shavuot needs Pesach in order to have a foundation in real life.
The two festivals are interconnected.
Whoever severs them remains with a partial entity, with only one aspect of things.
–Rabbi Adin Steinsaltz
From "Freedom without Content" in On Being Free by Rabbi Adin Steinsaltz