The third burial notice is regarding Eleazar the high priest. We haven't heard much about Eleazar in the Book of Joshua. But he had an important role in the distribution of Israel's inheritance. Why? If you recall, the distribution of the land was by casting lots to discern the will of God. This fell under Eleazar's responsibility as the high priest. When Joshua was appointed as Moses' successor, the Lord said, "And [Joshua] shall stand before Eleazar the priest, who shall inquire for him by the judgment of the Urim before the LORD." The Urim and the Thummim, which were sometimes simply called the Urim as here, were associated with the breastplate that the high priest wore (Lev. 8:8). This breastplate was also called "the breastplate of judgment" (Ex. 28:30) because it was used to divine God's will.
Why is Eleazar's death mentioned here? Joshua was the undisputed leader of Israel. But he was not the only one. There were elders. There were tribal leaders, too. But for the theocratic nation that Israel was, the role of the high priest was obviously one of the most important ones. In a theocratic nation, the church and the state are inseparably connected; in fact, the state is under the authority of its religion. The sanctuary is therefore not only the center of its religious life but also its national life as a whole. And it was the high priest who was in charge of the sanctuary and its worship. So then, the fact that Eleazar died would be notable news because of the significant role he played in the life of Israel. But it would not be anything extraordinary because everyone dies in the end. It was his turn.