Aaron's rod budded and God secured the Levitical priesthood.
After all of the rebellions and quarrels, you might think that the children of Israel had learned their lesson following Korah's rebellion. You would be mistaken.
GOD took additional measures, in response to Israel's stubbornness, to secure the priesthood with Aaron's family alone.
First, GOD had Israel make the censers of the 250 rebels who were consumed by fire into a cover for the altar.
1 Now the Lord spoke to Moses 2 and to Eleazar, the son of Aaron the priest, “Take up the copper censers out of the midst of those burned up, and scatter the strange fire there, so as to sanctify 3 the censers of those sinners—even the censers of the men who sinned at the cost of their lives—and make them into beaten plates, as a covering for the altar; so they might be brought before the Lord and sanctified, to become a sign to the children of Israel.” 4 And Eleazar the son of Aaron the priest took the copper censers which those burned up had brought, and they added these as a covering for the altar, 5 as a memorial to the children of Israel, that no outsider who is not of Aaron’s seed should put incense before the Lord and be like Korah and his insurrection, as the Lord said by the hand of Moses.
(Numbers 17:1-5 OSB)
Second, GOD responded to still more rebellion from Israel:
6 The next day the children of Israel murmured against Moses and Aaron, saying, “You killed the people of the Lord.” 7 Now it happened, when the congregation regrouped itself against Moses and Aaron, they hastened to the tabernacle of testimony; and the cloud covered it, and the Lord’s glory was seen. 8 Then Moses and Aaron entered the front of the tabernacle of testimony, 9 and the Lord spoke to Moses and Aaron, saying, 10 “Get away from the midst of this congregation, and I will utterly destroy them at once.” So they fell on their faces. 11 Then Moses said to Aaron, “Take the censer, put fire in it from the altar, throw incense on it, and carry it quickly to the camp, and make atonement for them; for wrath has gone out from the Lord’s face, and is beginning to strike the people.” 12 So Aaron took it as Moses told him, and ran into the assembly; and already the plague had begun among the people. So he threw in the incense, and made atonement for the people; 13 and he stood between the dead and the living; so the plague ceased. 14 Now those who died in the plague were fourteen thousand seven hundred, besides those who died because of Korah. 15 Then Aaron returned to Moses at the door of the tabernacle of testimony, and the plague ceased.
(Numbers 17:6-15 OSB)
Third, GOD used another object lesson, harkening back to the signs in Egypt, to show once and for all His selection of Aaron and his family as the priests:
16 After this, the Lord spoke to Moses, saying, 17 “Speak to the children of Israel and get a rod from them, a rod from each of their fathers’ houses, from all their rulers according to their fathers’ houses—twelve rods. Write each man’s name on his rod. 18 You shall also write Aaron’s name on the rod of Levi, for there is one rod that shall be given according to the tribe of their fathers’ houses. 19 Then you shall put them in the tabernacle of testimony before the ark of the testimony, where I will be known to you. 20 So it shall be, the man I choose, his rod will blossom; thus I will remove the murmurings of the children of Israel which they murmur against you.”
21 Then Moses spoke to the children of Israel, and each of their rulers gave him a rod apiece, for each ruler according to their fathers’ houses, twelve rods; and Aaron’s rod was in the midst of their rods. 22 Moses then put the rods before the Lord in the tabernacle of testimony. 23 Now it came to pass on the next day, Moses entered the tabernacle of testimony, and behold, Aaron’s rod for the house of Levi had sprouted and put forth buds, and had produced blossoms and yielded ripe almonds. 24 Then Moses brought out all the rods from before the Lord to all the children of Israel; and they looked, and each man took his rod. 25 The Lord then said to Moses, “Bring Aaron’s rod back before the testimonies, as a sign to the sons of the disobedient, and let their murmurings cease from before Me, lest they die.” 26 Thus did Moses; as the Lord ordered him, so he did.
(Numbers 17:16-26 OSB)
With these actions, GOD made it clear to Israel that Aaron's family were the approved priests.