Malkitzedek was no longer Kohen Gadol at the time, as it says in Nedarim 32b:
"Rabbi Zekharya said in the name of Rabbi Yishmael: The Holy One, Blessed be He, wanted the priesthood to emerge from Shem, so that his children would be priests, as it is stated: “And Melchizedek king of Salem brought forth bread and wine; and he was priest of God the Most High” (Genesis 14:18). Once Melchizedek, traditionally identified as Shem, placed the blessing of Abraham before the blessing of the Omnipresent, He had the priesthood emerge from Abraham in particular, and not from any other descendant of Shem. As it is stated: “And he blessed him and said: Blessed be Abram of God Most High, Maker of heaven and earth, and blessed be God the Most High” (Genesis 14:19–20). Abraham said to him: And does one place the blessing of the servant before the blessing of his master? You should have blessed God first. Immediately the Holy One, Blessed be He, gave the priesthood to Abraham, as it is stated: “The Lord says to my lord: Sit at My right hand, until I make your enemies your footstool” (Psalms 110:1), and afterward it is written: “The Lord has sworn, and will not repent: you shall be a priest forever, because you are a king of righteousness [al divrati malki tzedek]” (Psalms 110:4), which is explained homiletically to mean: Due to the improper words [divrati] of Melchizedek, the offspring of Abraham shall be priests of God forever."
After the War of the Four and Five Kings, Malkitzedek first blessed Avraham and only then Hashem, and for this he lost his priesthood (as the gemara in Yevamot 121b says: "the Holy One, Blessed be He, is exacting with His surroundings, i.e., the righteous who are close to Him, up to a hairsbreadth"), which was then given to Avraham. As such, Avraham had no need of another kohen in the area because he was the KG.