Mizbeiach chadash b'tzion tachin v'olas Rosh Chodesh naale alav u'sierei izim naaseh b'ratzon, a new altar establish in Tzion and the burnt offering of Rosh Chodesh will we offer upon it and goat we will offer willingly. The Dover Shalom explains that in order for the atonement of the sacrifices to return a new altar will first have to be established.

The Etz Yosef points out that the dimensions of this new altar are already given by the prophet Yechezkil in Chapter 45 of Sefer Yechezkial. The Rokeach says that this altar will be prepared by Hashem and descend ready-made from the heavens. He also relates that every Rosh Chodesh, the fires of gehenom are renewed and the Rosh Chodesh sacrifices affect the atonements and mitigation of these fires. According to the Etz Yosef, the burnt offering referred to here is a special burnt offering that the nasi, the king will bring in the future, as mandated in Sefer Yechezkial. It cannot refer to the regular burnt offerings of Rosh Chodesh since they were a total of 10; 2 bulls, 1 ram and seven sheep. Others say that Olas Rosh Chodesh means the unit of 10 burnt offerings brought on Rosh Chodesh.

Rav Refael of Homburg explains that the sin offering mandated by the Torah is one goat, however in the future many sin offerings will be brought to compensate for all the years the sacrifices were not brought. Hence, sieerei izim in the plural.

The Hearas Hatefillah adds that additional individual sin offerings will then be brought to atone for sins committed that required a sin offering when there was no Beis HaMikdash. However Rav Amram Gaon and so too the Maharit Al Gazi have the version seir izim in the singular. Rav Shamshon Refael Hirsch points out that these new sacrifices will be done willingly, with great intention and hence affect everlasting love as mentioned further on. To expand this idea, this is so since these sacrifices will be something new and fresh and inevitably something new and fresh is done with desire, enthusiasm and intention.

The Dover Shalom alternately explains that the goat sin offerings will be offered willingly i.e. voluntarily, since when Moshiach will come and the altar will be established, the world will have reached its perfection and the moon will be restored to its original size and luster and there will be no need to bring the sin offering that atoned for the diminishing of the moon. He also explains that although the sin offering always preceded the burnt offering, they are mentioned here in reverse order since only the slaughtering of the sin offering came before the slaughtering of the burnt offering but in their actual burning of the various parts of the animal on the altar which is referred to here, the burnt offering preceded the sin offering.

u'v'avodas Beis HaMikdash nismach kulanu, and in the service of the Beis HaMikdash we all will rejoice. The Siach Yitzchak explains that when then 2nd Beis HaMikdash was built some rejoiced not seeing the 1st Beis HaMikdash and those who saw the 1st Beis HaMikdash cried being sensitive to the lower level the 2nd Beis HaMikdash was on compared to the 1st Beis HaMikdash. However when the 3rd Beis HaMikdash will be built, which will be superior to the two that preceded it, everyone will rejoice. Alternately he explains that it was decreed on the generation that left Egypt and died in the desert that they would not merit to see the resting-place of the first Beis HaMikdash. Since that Mikdash was not fully destroyed but sank into the ground, if it were merely reestablished in the future the original decree would still apply and those people that died in the desert would not be able to rejoice in the building of the 3rd Beis HaMikdash. However since a new altar will be established to which the decree did not apply and then even that generation will be able to rejoice in the service of the Temple, hence all will rejoice.

The Dover Shalom explains that we do not merely to remember the sacrifices and recite them but rather to rejoice in the actual service that will be restored.

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