The Nechisti Council was the ruling body of the Nechisti Order, the religious body of the Nechani people. The Council had a centuries-long agreement with the Nechani government not to interfere in one another's affairs.
In 2373, the Nechisti Council approved Kathryn Janeway's request to undergo a sacred ritual for the purpose of saving Kes' life, following the example of the ancient King Nevad. They apparently found her "creative approach" fascinating, and considered it an honor that she would want to search for the Ancestral Spirits. (VOY: "Sacred Ground")