Benjamin waxes old, but he hasn’t begun to be old. That seems like a strange distinction, but “began to be old” is used to describe one about to die. For Benjamin, it may mean that he was aged, but we will learn that he lives for three more years. Where the transfer of kingship would typically come as the previous king is dying, Benjamin will instead abdicate. Because this description comes from Mormon, it may be his reasoning of why Benjamin would have called his son to be king. However, there are other elements that we will see which suggest that there was perhaps a different motivation.
Mosiah is brought before the king, who declares that Mosiah will be announced as the king and ruler over the people of the land of Zarahemla. This is to occur during a gathering of the people. That the gathering and transference of the title had an even greater reason can be seen when we understand that Benjamin did much more than seat his son as the next king.