He co-founded and serves as a senior faculty member at Yeshivat Birkat Moshe, the Hesder yeshiva of Maale Adumim.

[3] After Nadel's death in 2004, Sheilat published a compilation of his teachings entitled Betorato shel Rav Gedalia.

The book, however, was banned by three of the most respected spiritual leaders in the Haredi world, as it seeks to resolve apparent contradictions between science and Torah, accepting Charles Darwin's theory of evolution and other scientific views over biblical literalism.

[4] His wife, Yehudit Sheilat, is the director of Takana, a forum of prominent personalities fighting sexual abuse in the National Religious sector.

"[8] In 2018, Shilat published a book promoting his legal solution to the problems of Agunah and Get refusal by way of a new regulation (takanah).

He wrote Bein ha-Kuzari le-Rambam in 2010, comparing the philosophical approaches of Maimonides and Rabbi Judah Halevi.