During the period of the divided Kingdom of Israel, who were the priests who administered the Temple in Judah? I understand that the tribe of Levite was part of the northern Kingdom of Israel. Thank you.
If you look in the Book of Joshua, you will see that the Levites were not given a specific geographic territory. This was for spiritually symbolic reasons, as God’s priests, including all disciples who are priests, have their inheritance in “heaven,” not on the earth. Rather, they were given certain cities to dwell in (see Joshua Ch 21). Some of those towns were in Judah and Simeon. This is specifically mentioned in Joshua 21:4-5, 9. The Levites were scattered throughout Israel, including Gilead, across the Jordan. There were plenty of Levites in the South, and specifically the Kohathites, who were priests, in Judah. After Jeroboam took over Samaria, setting up bulls for sacrifice in Samaria and Dan, many of the Levites emigrated out of Samaria and into Judah, where they were presumably more welcome. By the time of the destruction of the Northern Kingdom, we can assume that the great majority of Levites and priests were already in Judah.
By the way, as an associated point, often one hears about the ten supposedly lost tribes (and by implication, only two of the tribes survived in the South). There is a slight grain of truth to the idea of lost tribes, but it is largely untrue. First of all, there were actually 13 tribes, counting the “half-tribes” of Ephraim and Menassah. Then there is the fact that all of Simeon, all of Benjamin and much of Dan were in the South, as well as most of the Levites and, of course, Judah were in the Southern kingdom of Judah. Therefore, at least five of the tribes had large populations in the Southern Kingdom of Judah. Also, we can reasonably assume that when Assyria conquered Samaria/the Northern Kingdom, many refugees from the other tribes ended up in Judah. For this reason, although several of the tribes were largely deported, never to return, most likely none of the tribes were completely “lost” when the kingdom of Samaria was destroyed. Of course, this includes the Levites about which you asked.