When Rosh Hashanah falls on Shabbat, one must remember that the obligation of Se置da Shelishit applies on that day no less than it does on any other Shabbat throughout the year. Besides the meal eaten after the morning service on Rosh Hashanah, one must also eat another meal consisting of at least a Ke鍛esa of bread after Minha, in fulfillment of the obligation to eat three meals on Shabbat. Therefore, it is proper for synagogues to schedule Minha prayer services earlier than usual in the afternoon of Shabbat Rosh Hashanah, in order to allow sufficient time for Se置da Shelishit.
The Rama (Rabbi Moshe Isserles of Cracow, Poland, 1525-1572) mentions that in such a case, when the first day of Rosh Hashanah falls on Shabbat, one should eat Se置da Shelishit before the ninth hour of the day. Since one must eat a Yom Tob meal on Mosa弾h Shabbat (the second night of Rosh Hashanah), and Halacha requires eating Shabbat and Yom Tob meals with an appetite, one must ensure to eat Se置da Shelishit on Shabbat Rosh Hashanah before the ninth hour of the day (as defined by Halacha). The Mishna Berura (Rabbi Yisrael Meir Kagan of Radin, 1839-1933) adds, however, that if a person did not eat Se置da Shelishit before the ninth hour, he should nevertheless eat the meal at that point. The obligation of Se置da Shelishit overrides the concern for entering the second day of Yom Tob with an appetite. Therefore, although it is preferable to eat Se置da Shelishit before the ninth hour of the day, one who did not should still eat Se置da Shelishit.
Summary: The requirement to eat Se置da Shelishit on Shabbat applies even when Shabbat is also Yom Tob. Therefore, when the first day of Rosh Hashanah falls on Shabbat, Minha should be recited earlier than usual to allow time for Se置da Shelishit, which should preferably be eaten before the ninth hour of the day.
