According to orthodox rabbinical authorities, who wrote the Zohar Hadash?
In the same style as the Zohar; there are numerous Rabbis/Sages that give over teachings.
These Rabbis include Rabbi Shimon, Rabbi Yehudah, Rabbi Elazar, Rabbi Yitzhak, and others from the Zohar.
As far as to who actually recorded the teachings, in parshas Haazinu, Rabbi Shimon says: “I am arranging you as follows: Rabbi Abba will write, Rabbi Elazar, my son, will study orally, and the rest of the friends will converse in their hearts” (Zohar, Haazinu).
Therefore, it can be deduced that since the teachings in the Hadash all stem from the same era, that Rabbi Abba recorded those as well.
As background to answering this question, we need to give a little history of the Zohar. The Zohar was "written" by Rabbi Shimon Bar Yochai and his students. Unlike the Mishna and the standard Midrashim, it was not a published work. The Zohar was probably passed only orally to select students. The Mishna and Midrashim most likely were also passed down essentially orally for many centuries, but in a public fashion. Even if the Zohar had been recorded in writing, there were not many copies for many centuries. After the initial spread of the Zohar by Moshe De Leon, many manuscripts were written. These manuscripts did not all have the same content, and many passages were in some copies and not in others.
When the Zohar was first printed, incomplete manuscripts were used. Parts of the Zohar that were in other manuscript editions that were only printed later were called the Zohar Chadash. This is what it says on the title page of the first printing. The newness is only about when it was printed, not about when the contents were originally written.