I don't think I've ever heard the word "Apostolic" used in relation to Rabbinic Judaism:
By the end of the 2nd century, perhaps in response to Church Father Irenaeus's notion of apostolic succession, the rabbis proclaimed a chain of authority that they attributed to the earlier synod of Yavneh. Both the early Christian and rabbinic cultures were constructing parallel frameworks of leadership based on the shared Hellenistic idea of diadoche, a record of succession linking established teachers with a larger school of thought, while tracing their lineage back to its founder. In the mishnaic text, Pirkei Avot, "Ethics of the Fathers," the rabbis constructed a chain of oral tradition beginning with the revelation at Mt. Sinai to Moses, who passed it on to Joshua, who handed it down to the Elders, who transmitted it to the Prophets and finally to the men of the Great Assembly. These Palestinian rabbis claimed that the process of rabbinic ordination had already begun with Moses, whom they referred to as Moshe Rabbeinu, "our rabbi." Based on their exclusive claim to the Oral Law transmitted from God to Moses and passed down through the chain of tradition, the rabbis were able to permanently legitimize their political and religious power.