The Forever Pact

Rashi: "It shall be":
This covenant of Mine [mentioned in the previous verse] shall be for him.

"an eternal covenant of kehuna":
Although the kehunah had already been given to Aaron’s descendants, it had been given only to Aaron and his sons who were anointed with him, and to their children whom they would beget after their anointment. Pinchas however, who was born before that and had never been anointed, had not been included in the kehunah until now. And so, we learn, "Pinchas was not made a kohen until he killed Zimri." (Zevachim 101b)

"for his G‑d":
meaning for the sake of his G‑d, as in (11:29), "Are you zealous for my sake?" and (Zech. 8:2), "I am zealous for Zion"- meaning for the sake of Zion.

Ohr HaChayim: "he atoned on behalf of the children of Israel'
He reestablished peace between Israel and their Father in Heaven and enabled the children of Israel not fear the Angel of Death. Therefore, his people made a peace pact with him. Just as this benefit to them extended from generation to generation, so Pinchas' elevation to the priesthood also extended forever.

Too, we learn from our Sages that Elijah the prophet who will usher in Mashiach, who was (a reincarnation of) Pinchas. In the future, Pinchas will merit to bridge the generation gap between fathers and sons, harmonizing their relationships, as his principal function is to increase Shalom in the world.

Maggid Mesharim: "When he avenged my jealousy":
This was said with regard to the sin that blemished the covenant that was poured into the daughter of a Gentile. And this caused the jealousy, as our Sages said, "A woman is jealous only of the thigh..." Now since abundance that was due her was poured into a daughter of a Gentile, and she (Cozbi's daughter) was like "a maidservant who inherits in the place of her mistress." (Proverbs 30:23) Certainly this aroused the jealousy of the Shechinah. Pinchas avenged this jealousy because he put on the clothing of malchut, the jealousy of malchut betocham "in their midst", that is, he dressed up the letter מ--Mem which represents malchut and actually took upon himself the jealousy of malchut. The מ--Mem hints to malchut because it is the first letter of the word malchut as well as the final letter in Betocham. This is the secret of the 40 [the gematria of Mem] se'ahs of water in a kosher mikveh.

...he set his life in the balance by dedicating himself heart and soul to the recovery of the nation... Zrizuta D'Avraham: Rashi says that Pinchas had not been a Kohen since he himself wasn't anointed like Aaron and his sons, and was born too early to inherit the priesthood as one of Aaron's children. But when he set his life in the balance by dedicating himself heart and soul to the recovery of the nation, he became born anew and thereby worthy of being a Kohen, as if he had been born in the right time to be anointed himself. Pinchas then served with Aaron, Aaron's sons, and the other children like an uncle of the priests. All 99 high priests in the First and Second Temples descended from Pinchas. When anyone gives themselves heart and soul to save their people, they are born anew, capable of functioning in activities formerly reserved for those born with ties in the right places. (Peninei HaChassidut)

Lubavitcher Rebbe: The Zohar [on page 213, below] teaches that the letter Yud was added to Pinchas' name and the letter Hei was added to Joseph's name because they were both zealous about the prohibition of cohabiting with a non-Jewish woman. Pinchas killed Zimri, and Joseph resisted the persistent attempts of Potiphar's wife. This illuminates Rashi’s explanation why each the family name included in the national census had a Hei at the front, and Yud at the end: "The nations would taunt Israel saying, 'Why do they trace their lineage by tribe? Do they really think that the Egyptians did not have their own way with their mothers? So G‑d placed His Name upon them, Hei at one side and Yud at the other to say 'I testify that these people are indeed the sons of their fathers." (Ibid. 26:5) These same letters Yud and Hei were added to show the Jewish people were as righteous as Pinchas and Joseph.

Our Sages note that the Hebrew words for man and woman –ish, isha--differ only in the letters Yud and Hei, which together spell G‑d's Name. "If a couple is found worthy, G‑d's Presence will be with them." (Sota 17a.) This is an even earlier source that Yud and Hei testify that G‑d's people are pure and holy.

Zohar Pinchas 213:
Rabbi Yesa said: Whoever respects the name of his Master in this matter, and keeps it [the covenant, i.e. circumcision] is privileged to have his Master respect him over all. How do we know this? Because regarding Joseph, it is written, "And he made him to ride in the second Chariot which he had...and made him ruler over all the land of Egypt." (Gen. 41:43) Furthermore, when Israel crossed the sea, Joseph's coffin entered the water first and the waters in front of it were unable to stay as they were. Therefore it is written, "The sea saw it, and fled." (Psalms 114:3) What is the meaning of "and fled"? The sea saw him about whom this is written, "and fled, and went outside." (Gen. 39:12)

Come and see: He was honored in his life and in his death. Why in his life? Because during that time he did not want to cleave as it is written: "But he refused, and said to his master's wife..." (Gen. 39:8) As it is written, "that he hearkened not to her, to lie by her, or to be with her." (Gen. 39:10) For this reason he was honored in this world, for it is written, "And she caught him by his garment...and he fled, and went outside." He earned entry after death into the heavenly curtain. And so it was befitting to him, that he received his due in this world and in the other world.

Pinchas was privileged in this world and in the next, and was enabled to live and exist longer than all those who came out of Egypt. He also merited to serve as High Priest, both he and all his sons after him. However, this is incorrect; there are those who say that he had earned the priesthood previously. If so, how should we understand the words, "because he was zealous for his G‑d"? (Num. 25:13) whose meaning is that he earned the priesthood because of this deed and had not gained it previously.
...any priest who kills a person is considered forever unfit for the priesthood...
Come and see: any priest who kills a person is considered forever unfit for the priesthood because he has marred his own status; thus Pinchas was legally barred from remaining a priest. But because he was zealous for G‑d, He had to reinstate him, and also his seed after him for all time, into the priesthood. Rabbi Yitzhak said, Come and see: Pinchas is recorded above and below, before he came into the world. The reason his deeds were recorded is that he was among those who came out of Egypt