Below you will find what the Kollel wrote about that in our Background to the Daf for Sanhedrin 84. I hope it helps you.

Best wishes,

Mordecai Kornfeld

Kollel Iyun Hadaf

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8) [line 2] ZAKEN MAMREI AL PI BEIS DIN (ZAKEN MAMREI)

(a) A Zaken Mamrei is a Torah Sage who argues against and defies the ruling of the Great Sanhedrin of 71 judges of the Lishkas ha'Gazis in Yerushalayim, with regard to a practical Halachic decision. The Torah states, "veha'Ish Asher Ya'aseh v'Zadon l'Vilti Shemo'a El ha'Kohen... O El ha'Shofet, u'Mes ha'Ish ha'Hu..." - "And the man who will act presumptuously, and will not listen to the Kohen... or to the judge, that man shall die..." (Devarim 17:12).

(b) Chazal received the tradition that a Sage does not become a Zaken Mamrei unless the following conditions are met:

1. He is one of the outstanding Torah Sages of his time, authorized to judge and to teach Halachic matters.

2. He was involved in a dispute with other Sages in a Halachic matter, and they brought the case to the Great Sanhedrin for judgment.

3. The Sanhedrin ruled against him, but he nevertheless returned to his city and obstinately continued to rule according to his own opinion.

(c) If these three conditions are fulfilled after having received the proper warnings, he is termed a Zaken Mamrei and is put to death by Chenek (choking). His sentence is carried out in Yerushalayim when Benei Yisrael come for Aliyah la'Regel, on the next holiday, to fulfill the verse, "v'Chol Yisrael Yishme'u v'Yira'u, v'Lo Yezidun Od." - "And all the people of Yisrael shall hear, and fear, and do no more presumptuously [inspired acts]." (ibid. 17:13)