Reference for Rosh Hashanah 4:7
הָעוֹבֵר לִפְנֵי הַתֵּבָה בְּיוֹם טוֹב שֶׁל רֹאשׁ הַשָּׁנָה, הַשֵּׁנִי מַתְקִיעַ. וּבִשְׁעַת הַהַלֵּל, רִאשׁוֹן מַקְרֵא אֶת הַהַלֵּל:
The prayer leader on the yom tov of Rosh Hashanah — the second officiates at the blowing of the shofar [i.e., The prayer leader at mussaf officiates at the shofar blowing, and not the shacharith prayer leader. This was instituted at a time of shmad (enforced conversion), when they decreed against blowing the shofar and lay in wait for them all six hours of the time of the shacharith prayer, whereupon they moved the shofar blowing from shacharith to mussaf.]; and at the time of Hallel, the first officiates at the Hallel. [Because Hallel is not recited on Rosh Hashanah and Yom Kippur, we have "and at the time of Hallel"; that is, on the other festivals, when Hallel is recited.]