Genesis and Ancient Israel
The noun nasi occurs 132 times in the Masoretic Text of the Hebrew Bible, and in English is usually translated "prince," occasionally "captain." The first use is for the twelve "princes" who will descend from Ishmael, in Genesis 17, and the second use, in Genesis 23, is the Hethites recognising Abraham as "a godly prince" (nasi elohim נְשִׂיא אֱלֹהִים). Later in the history of Ancient Israel the title of nasi was given to the political ruler of Judea - e.g. Lev 4:22; Ezek 44:2-18; Ezra 1:8 (comp. Yer. Hor. 3:2).
Second Temple period
During the Second Commonwealth (c. 530 BCE - 70 CE), the nasi was the highest-ranking member and president of the Sanhedrin or Assembly, including when it sat as a criminal court. The position was created in c. 191 BCE when the Sanhedrin lost confidence in the ability of the High Priest to serve as its head.The Romans recognised the nasi as Patriarch of the Jews, and required all Jews to pay him a tax for the upkeep of that office, which ranked highly in the Roman official hierarchy.'
Late Roman empire to medieval period
'This position as patriarch or head of court was reestablished by the Romans after the Bar-Kokhba revolt in 135 CE.This made ha-Nasi a power which both Jews and Romans respected. The Jewish community in Babylonia also recognized him. The Nasi had controlled leadership and served as a political representative to the authorities while the religious leadership was led by Torah scholars. The Nasi had the power to appoint and suspend communal leaders inside and outside of Israel. The Romans respected the nasi and gave extra land and let control of own self-supported taxes'
The term nasi was later applied to those who held high offices in the Jewish community and Jews who held prominence in the courts of non-Jewish rulers. Certain great figures from Jewish history have used the title, including Judah the Prince (Judah haNasi), the chief redactor of the Mishnah.
The nasi were also prevalent during the 8th century Frankish kingdom. They were a highly privileged group in Carolingian France. The Jews have collaborated with King Pepin to end Muslim rule over their city in 759. The Jews accepted surrender and Pepin was able to hold off the Saracens in Spain. Pepin rewarded the Jews with land and privileges such as the right to judicial and religious autonomy under rule of their own leadership. The heirs of the King and nasi held a close relationship until the tenth century.
'In Modern Hebrew, nasi means president, and is not used in its classical sense. The word for prince is now nasich. Much more recently, Rabbi Adin Steinsaltz has taken the title nasi, in an attempt to re-establish the Sanhedrin in its judicial capacity as the Supreme Court of Judaism.'
If you really want to learn about something, the internet allows us to do the research. And in this learning experience we will learn more. For instance, I did not know 'Rabban was a higher title than rabbi' and was given to the nasi starting with Gamaliel the Elder..
Starting with Rabbi Judah I haNasi (born 135 CE), not even the nasi was given the title rabban. In its place, Judah haNasi was given the lofty accolade Rabbeinu HaKadosh ('Our Holy Teacher').
Peace be with you