In seems the prince will be the one offering sacrifices during the feasts,but nothing is mentioned of the day of atonement.
Ezekiel 45:17 (KJV)
17 And it shall be the prince's part to give burnt offerings, and meat offerings, and drink offerings, in the feasts, and in the new moons, and in the sabbaths, in all solemnities of the house of Israel: he shall prepare the sin offering, and the meat offering, and the burnt offering, and the peace offerings, to make reconciliation for the house of Israel.
Ezekiel 45:21-23 (KJV)
21 In the first month, in the fourteenth day of the month, ye shall have the passover, a feast of seven days; unleavened bread shall be eaten. 22 And upon that day shall the prince prepare for himself and for all the people of the land a bullock for a sin offering. 23 And seven days of the feast he shall prepare a burnt offering to the LORD, seven bullocks and seven rams without blemish daily the seven days; and a kid of the goats daily for a sin offering.
Ezekiel 45:25 (KJV)
25 In the seventh month, in the fifteenth day of the month, shall he do the like in the feast of the seven days, according to the sin offering, according to the burnt offering, and according to the meat offering, and according to the oil.
Will the prince also officiate during the day of atonement