The first Ramban in the parsha makes an interesting statement. He explains that Hashem informed Moshe that He would reward Pinchas for "avenging the vengeance of Hashem," and for the kindness that he performed for Bnei Yisrael by preventing all of them from dying in the plague. Moreover, Hashem commanded Moshe to inform Bnei Yisrael that Pinchas would be a Kohein Gadol forever!
Rav Wolbe (Shiurei Chumash) comments that at that time Elazor filled the position of Kohein Gadol. We know that there can be only one Kohein Gadol at a time, so what does the Ramban mean by asserting that Pinchas would always be a Kohein Gadol? (For this reason some versions actually delete the word "Gadol").
A similar same question could be asked regarding the wording of "al hanisim." We say, "Bi'mei Mattisyahu ben Yochanon Kohein Gadol." Yet, historical records indicate that Mattisyahu was not a Kohein Gadol! Because of this problem, the Reform Movement deleted that word from al hanisim!
However, says Rav Wolbe, the Reform Movement simply misunderstood Chazal. When they gave Mattisyahu the title of Kohein Gadol, they didn't mean that he filled the position of Kohein Gadol and served as the highest ranking Kohein in the Bais Hamikdosh. Chazal were describing the accomplishments of Mattisyahu. When he fought against the Hellenists, he was acting in a fashion which is exemplified by the Kohein Gadol.
This is also the intention of the above Ramban. When Pinchas killed Zimri, he was given the appellation Kohein Gadol not because he was to serve in the Mishkan on Yom Kippur, but rather, since he acted with the greatness (gadlus) that is the hallmark of a Kohein Gadol. As the Ramban continues, Pinchas was worthy of such a reward because he killed both a Nasi and the daughter of a king and did not fear them due to his great vengeance for Hashem. A Kohein Gadol stands up for Hashem's honor no matter whom he is up against.
Accordingly, the right to the title Kohein Gadol is not limited to selected descendants of Aharon who lived in the times of the Bais Hamikdosh. Every person has the ability to become a Kohein Gadol. Standing up for Hashem's glory even when it might cost one his prestige (or even his life) earns one the appellation Kohein Gadol! There are numerous occurrences, even on a daily basis, that present an opportunity for a person to stand up for Hashem's honor. Asking someone to turn off his phone in the Bais HaMedrash, motioning that it is forbidden to speak during davening, and softly reminding someone that we shouldn't speak lashon hara are just a few. As the Torah tells us regarding Pinchas, the reward for such actions is immense!