After prophesying of the millennium, Isaiah prophesies of a second great gathering of Israel, the first one being the exodus from Egypt (see also Jeremiah 16:14–16). This gathering commences before the Second Coming, but probably continues into the millennium.
The root of Jesse is identified in Doctrine and Covenants 113:5–6 as “a descendant of Jesse, as well as of Joseph, unto whom rightly belongs the priesthood, and the keys of the kingdom, for an ensign, and for the gathering of my people in the last days.” The fact that these keys of the kingdom were given to Joseph Smith for time and eternity (D&C 90:2–4 partially quoted above) helps us identify him as the servant. Joseph being spoken of twice in the same chapter has led some to feel it must be a different person spoken of in the second reference. However, Joseph is spoken of in a different mission than the first. His second mission was to fulfill the covenant made to Abraham. In 1841 the Lord revealed to Joseph:
58 And as I said unto Abraham concerning the kindreds of the earth, even so I say unto my servant Joseph: In thee and in thy seed shall the kindred of the earth be blessed. [D&C 124:58]
Just as Isaiah prophesied of another mission for Joseph after telling of his first, the Lord waited until the first mission was completed before informing Joseph of the second mission (he knew before 1841 as shown below). The blessing of all the kindred of the earth included taking the gospel to the Gentiles. Paul quoted the Isaiah passage (Isaiah 11:10), with slightly different wording, as evidence that the Gentiles were to receive the gospel.
This wording also helps to identify the servant as Joseph Smith; “And again, Esaias saith, There shall be a root of Jesse, and he that shall rise to reign over the Gentiles; in him shall the Gentiles trust” (Romans 15:12). Joseph Smith was designated to reign over the Gentiles as shown below.