After the death of Irdan-bey in 1762, Suleiman-bek was declared the ruler of the Kokand Khanate, who reigned for only a few months. After that, power passed into the hands of the grandson of Abdukarim-biy Narbuta-biy. He ascended the throne at the age of 14. As historians write, Narbuta-biy renounced power for a long time, but then representatives of the Kokand nobility persuaded him to become a ruler.

Narbuta-biy established peaceful relations with the Emir of Bukhara Shahmurad. And also, had diplomatic relations with the King Empire between 1774-1798.

Narbuta-biy was the patron of science and arts. At that time, active construction was carried out in Kokand. In 1798, the construction of the Narbuta-biy madrasah was completed in Kokand. In the era of Norbutabiya, several madrasahs were built: In 1762 - Sulaimoniya Madrasah, in 1789 - Eshon Khonkhuzha, in 1794 - Imam Bakir, in 1795 - Tura Hakim, in 1798 - Madrasai Mir, among these buildings of the madrasah named after Norbut-biy. It has survived to the present day and is also known as Madras-i Mir.

In the era of Norbuta-biy, famous cultural figures lived and worked in Kokand. Of these, Mukhammad Gazi, Nadir, Khujamnazar Khuvaido, Khozha Maslalhatuddin Ummatvali, and his son Khozha Mukhammad Nosiruddin ... Norbuta-bi bowed to Khozha Mukhammad Nosiruddin and Khozha Mukhammad Yakub Okhund throughout his life and was their murid. His sons: Mukhammad Amin, Mukhammad Olim and Mukhammad Umarkhan also gave into the hands of Mukhammad Nosiruddin for education.

After the death of Norbuta-biy in 1798, his son Alimkhan was declared the ruler of the state.