Rosh Hashanah, Chapter 4, Mishnah 7: "Ha'over lifnei ha'teivah b'yom tov shel Rosh Hashanah - ha'sheni matkia" - the one who passes before the ark on the festival of Rosh Hashanah: the second leader sounds the shofar. The second chazzan, the one who leads the Mussaf prayer, is the one during whose prayer the shofar blasts are sounded - the blasts are woven into his Shemoneh Esrei, and he is the one leading the prayer in which the blasts take place.
The reason given in the Gemara:
The Gemara explains that it was not always this way. Originally the shofar was sounded as part of Shacharis, and therefore Malchiyos, Zichronos and Shofaros were said at Shacharis. But the enemies of Israel decreed against the sounding of the shofar and against the observance of the mitzvos, and they stationed spies in the synagogues to make sure that no shofar would be sounded. The spies would wait around for a long stretch of time, and when no blast was heard at Shacharis they would give up and leave; by the time Mussaf came, the Jewish people were able to sound the shofar. From then on the blasts were moved to the Mussaf prayer.
The conclusion of the Mishnah - Hallel:
The Mishnah concludes with the matter of Hallel - on those occasions when Hallel is said, since on Rosh Hashanah itself Hallel is not recited: "Ha'rishon makrei es ha'Hallel" - the first leader recites the Hallel. The first chazzan, who leads Shacharis, is the one who leads Hallel, since Hallel is said at Shacharis and not at Mussaf.
In summary: in this Mishnah we learned how the roles are divided between the prayer leaders on the festival of Rosh Hashanah: the shofar blasts were given over to the second leader, at Mussaf, because of the enemies' decree that caused the blasts to be moved from Shacharis to Mussaf; while Hallel, which is said at Shacharis, was given over to the first leader.