The prayer service that follows Shacharit and includes extra Rosh Hashanah liturgy is Musaf, also spelled Mussaf.
Musaf is an additional service recited on Shabbat, Jewish festivals, Rosh Chodesh, and Rosh Hashanah. Its historical basis is traditionally connected with the extra offerings brought in the Jerusalem Temple on special days. In modern synagogue practice, the service includes an additional Amidah rather than sacrifices.
Rosh Hashanah’s Musaf is especially distinctive. Its Amidah has nine blessings, including three central sections known as Malchuyot, Zichronot, and Shofarot— themes of divine kingship, remembrance, and the shofar. In many traditional communities, the shofar is sounded during the repetition of this prayer. Mincha is the afternoon service, Maariv is the evening service, and Kabbalat Shabbat welcomes Shabbat, so none is the service described here.