Берешит 23:3 Мидраш: Bamidbar Rabbah, Midrash Tanchuma, Midrash Tanchuma Buber & Vayikra Rabbah

“…and they had no children. Elazar and Itamar served as priests.” Rabbi Yaakov bar Aivu in the name of Rabbi Aḥa: If they had sons, they would have taken precedence over Elazar and Itamar, as whoever takes precedence for inheritance takes precedence regarding honor, provided that he conducts himself in accordance with the custom of his fathers.
“Elazar and Itamar served as priests in the presence of [al penei] Aaron, their father.” Rabbi Yitzḥak said: During his lifetime; Rabbi Ḥiyya bar Abba said: After his death. According to the opinion of Rabbi Yitzḥak, who said during his lifetime, here, it is stated al penei and there it is stated al penei, as it is written: “Haran died al penei Teraḥ his father” (Genesis 11:28). Just as al penei stated there is during his lifetime, so, too, al penei that is stated here is during his lifetime. According to the opinion of Rabbi Ḥiyya bar Abba, who said after his death, here, it is stated al penei and there it is stated al penei, as it is written: “Abraham rose from al penei his dead” (Genesis 23:3). Just as al penei stated there is after death, so, too, al penei that is stated here is after his death. According to the opinion of Rabbi Yitzḥak, who said during his lifetime, if impurity befell Aaron, Elazar served; if impurity befell Elazar, Itamar served.
There was an incident involving Shimon ben Kimḥit who went out to speak with the king of the Arabs, and a drop of saliva sprayed from his mouth onto his garments and impurified him. Yehuda, his brother, entered and served in his stead in the High Priesthood. That day, their mother saw her two sons as High Priests. The Sages taught: Kimĥit had seven sons, and all of them served in the High Priesthood. The Sages said to her: ‘What good deeds do you have to your credit?’ She said to them: ‘So help me, in all my days, the beams of my house never saw the hair of my head.’ They said: ‘All flour [kimḥa] is flour [kimḥin], but Kimḥit’s flour [kimḥa] is fine flour.’ They read this verse in her regard: “All the glory of the king’s daughter is within” (Psalms 45:14).
According to the opinion of Rabbi Ḥiyya bar Abba who said: After his death, when Aaron died, Elazar his son served. When Elazar died, Itamar served. That is why it is stated: “Elazar and Itamar served as priests al penei Aaron, their father.”

(Numb. 3:4:) “And they had no children.” R. Jacob bar Abin said in the name of R. Aha, “If they had had children, they would have taken precedence over Eleazar and Ithamar, since whoever takes precedence with respect to inheritance takes precedence with respect to honor, provided that he follows the behavior of his forebears.”⁵⁰PRK 26(27):10; Lev. R. 20:11; Numb. R. 2:26. (Ibid.:) “So Eleazar and Ithamar served as priests in the presence of ('al-pene) their father Aaron.” R. Isaac said, “During his lifetime”; but R. Hiyya bar Abba said, “At his death.” According to the opinion of R. Isaac, who said, “During his lifetime,” 'al-pene is mentioned here, and pene is also mentioned elsewhere (in Gen. 11:28), “And Haran died in the lifetime of ('al-pene) his father Terah.” If pene as used elsewhere (i.e., in Gen. 11:28) [means] during his lifetime, pene as used here (in Numb. 3:4) also [means] during his lifetime. According to the opinion of R. Hiyya bar Abba, who said, “At his death,” pene is used here (in Numb. 3:4) and pene is used elsewhere (in Gen. 23:3), “Then Abraham arose from beside ('al-pene) his dead (i.e., his dead wife).” If pene as used elsewhere (in Gen. 23:3) [means] at his death, pene as used here (in Numb. 3:4) also [means] at his death. Now according to the opinion of R. Isaac, who said, “during his lifetime,” [when] uncleanness befell Aaron, Eleazar ministered; [when] uncleanness befell Eleazar, Ithamar ministered. There is a story about Simeon ben Gimhit,⁵¹He was high priest in 17-18 C.E. that he went out to speak with the king of the Arabians.⁵²TYoma 4(3):20; yYoma 1:1 (38d); yMeg. 1:12(10) (72a); yHor. 3:3/5(2) (47d): Yoma 47a; ARN, A 35:4. When a streak of saliva squirted from [the king's] mouth onto his clothes and rendered him unclean, his brother Judah entered and ministered in the high priesthood in his place. That day Gimhit saw two of her sons as high priests. They said, “Gimhit had seven sons, and all of them ministered in the high priesthood.” The sages entered her home and said to her, “Tell us what good deeds you have to your credit?” She said to them, “By the Temple service, the rafters of my house have never seen the hair of my head.” They say, “All flours (qimhayya) are flour (qimhin), but the flour of Gimhit is fine flour.” In reference to her they read this verse (Ps. 45:14), “All glorious is the king's daughter within; her clothing is of gold brocade.” Now according to the opinion of R. Hiyya bar Abba, who said, “At his death,” when Aaron died, Eleazar ministered; when Eleazar died, Ithamar served in his place. R. Abba bar Abbina said, “For what reason is the parashah [about the death of] of Miriam (Numb. 20:1) near the parashah of the ashes of the [red] heifer (Numb. 19:1ff.)?⁵³PRK 26(27):11; Lev. R. 20:12; yYoma 1:1 (38b); MQ 28a. Simply to teach that just as the ashes of the [red] heifer atones, so does the death of the righteous atone.” R. Judan said, “For what reason is the death of Aaron (Deut. 10:6) near the breaking of the tablets (Deut. 9:17)? To teach that the death of the righteous is as grievous to the Holy One, blessed be He, as the breaking of the tablets.” R. Hiyya bar Abba said, “The sons of Aaron died on the first of Nisan.⁵⁴According to Lev. 10:1, they died at the time of the dedication of the Tabernacle; and according to Exod. 40:17, the dedication began with its erection on the first day of the first month, i.e., on the first of Abib, which came to be called Nisan. For what reason does it mention their death on the Day of Atonement (in Lev. 16:1)? It is simply to teach that, just as the Day of Atonement atones, so does the death of the righteous atone.” And where is it shown that the Day of Atonement atones? Where it is stated (in Lev. 16:30), “For on this day atonement shall be made for you to cleanse you.” And where it is shown that the death of the righteous atones? Where it is stated (in II Sam. 21:14), “Then they buried the bones of Saul […] and God responded to the plea of the land thereafter.”

(Ibid.:) SO ELEAZAR AND ITHAMAR SERVED AS PRIESTS IN THE PRESENCE OF ('al-pene) THEIR FATHER AARON. R. Isaac said: During his lifetime; but R. Hiyya bar Abba said: At his death. According to the opinion of Rabbi Isaac, who said: During his lifetime, 'al-pene is mentioned here, and pene is also mentioned elsewhere (in Gen. 11:28): AND HARAN DIED IN THE LIFETIME OF ('al-pene) HIS FATHER TERAH. If pene as used elsewhere (i.e., in Gen. 11:28) < means > "during his lifetime," pene as used here (in Numb. 3:4) also < means > "during his lifetime." According to the opinion of R. Hiyya bar Abba, who said: At his death, pene is used here (in Numb. 3:4) and pene is used elsewhere (in Gen. 23:3): THEN ABRAHAM AROSE FROM BESIDE ('al-pene) HIS DEAD (i.e., his dead wife). If pene as used elsewhere (in Gen. 23:3) < means > "at his death," pene as used here (in Numb. 3:4) also < means > "at his death." Now according to the opinion of R. Isaac, who said: During his lifetime: If uncleanness befell Aaron, Eleazar ministered; if uncleanness befell Eleazar, Ithamar ministered. There is a story about Simeon ben Qimhit,⁵⁴He was high priest in 17–18 C.E. that he went out to speak with the king of the Arabians.⁵⁵TYoma 4(3):20; yYoma 1:1 (38d); yMeg. 1:12(10) (72a); yHor. 3:3/5(2) (47d): Yoma 47a; ARN, A 35:4. When a streak of saliva squirted from < the king's > mouth onto his clothes and rendered him unclean, his brother Judah entered and ministered in the high priesthood in his place. That day Qimhit saw two of her sons as high priests. They said: Qimhit had seven sons, and all of them ministered in the high priesthood. The sages entered her home and said to her: Tell us what good deeds you have to your credit? She said to them: By the temple service, the rafters of my house have never seen the hair of my head. They say: All flours (qimhayya) are flour (qimhin), but the flour of Qimhit is fine flour. In reference to her they read this verse. (Ps. 45:14 [13]): ALL GLORIOUS IS THE KING'S DAUGHTER WITHIN; [HER CLOTHING IS OF GOLD BROCADE].