Father-Son Chief Rabbi History
Rav Yitzhak Yosef Shlit"a, who was appointed as Rishon Letzion, is, of course, the son of Rav Ovadia Yosef Shlit"a. The appointment of both father and son as Rishonim Letzion is not unprecedented. However, it hasn't happened in 94 years.
According to Wikipedia Hebrew's List of Rishonim Letzion, Rav Yaakov Sha'ul Elyashar ZT"L was Rishon Letzion from 1893-1906. His son, Rav Hayim Moshe Elyashar ZT"L was Rishon Letzion from 1919-1921. (According to the list in English, however, Rav Hayim Moshe Elyashar was Rishon Letzion from 1914-1915. I would guess that the Hebrew version is more authoritative. Also, a different Wikipedia page says "Nissim Danon—In 1917, Palestine was occupied by the British. Danon was succeeded as chief rabbi after WWI by Haim Moshe Eliashar who assumed the title of Acting Chief Rabbi.")
See an article (in Hebrew) and a video of Rav Ovadia Shlit"a praising his son, Rav Yitzhak. He said to his son to care for the Agunot and have Ahavat Yisrael. He concluded by saying that he is not just a rabbi of Haredim or just for the religious, but a rabbi of all of Israel.
On the Ashkenazic side, Rav David Lau Shlit"a is the son of former Chief Rabbi Yisrael Meir Lau Shlit"a, the first such father-son pair for the much-more-recently-established Ashkenazic Chief Rabbinate. See an article (in Hebrew) and a video where the elder Rav Lau also praised his son, and noted that Rav David Lau is the 39th (!!!) generation of rabbis in his lineage, but the first born in Israel.