Rabbi Kaganoff answers your questions and says:
The Torah Writings of Rabbi Yirmiyohu Kaganoff
WHAT DO I DO WITH MY ESROG [after Shmita]
For the most part, those living in North America are concerned less
about whether they may import esrogim from Eretz Yisroel [after
Shmita], and more about what to do with such an esrog after Sukkos.
The esrog keeps its kedushas shvi’is until it becomes inedible, and
one may not actively facilitate its decay process nor ruin it in any
According to one approach suggested by the Tzitz HaKodesh, one may
be required to ship the esrog back to Eretz Yisroel after Sukkos.
However, most authorities do not require this.
Assuming that return shipping is not required, one still may not
destroy the esrog after Sukkos, but one is not required to preserve
it. Therefore, the simplest solution is to remember not to wrap up the
esrog on Hoshanah Rabbah. Without wrapping or refrigeration, the esrog
will soon dry out and become inedible. At that point, one may dispose
When we look around the shul on Sukkos and see everyone holding his
own set of arba’ah minim, we should sing praises to Hashem for helping
us fulfill these mitzvos so easily in comparison to earlier times,
when it was common for an entire community to share one set. At the
same time, we should remember the modern farmer in Israel who observed
shmittah with true mesiras nefesh, thereby attesting to the message of
shmittah — that the Ribbono Shel Olam created the world in six days
and rested on the seventh.
Another post says
Beth Israel - Malden - Annual Halacha Guidebook -
Rabbi Yitzchak Zev Rabinowitz
Important Notice Regarding Your Etrog - This year has been the Shmitta
year in Israel and its produce has a special sanctity. If your Esrog
is from Israel you may not dispose of it after Sukkot as you normally
would, it must be dried out completely before you may dispose of it.
Therefore, at the conclusion of using your etrog, leave it open to the
air which will help it dry out. It should take a couple of weeks for
it to dry out.