We are the continuation of the church first identified through the revaluation given to Joseph Smith, who was chosen by the Lord to establish His church in 1830. That Church became known as the Mormon Church.
At the prophet's death, that original church split into various factions, the largest of which became The Church of Jesus Christ of Latter-day Saints (note the hyphen). We are not, however, affiliated with that church based in Salt Lake City, Utah.
We are in a sense new, in that we are beginning to shout this newly revealed information to everyone. The first Utah branch was recently organized in April, 2020. But we are old, in that we are called by the Lord to go back to the original doctrine and authority God gave to Joseph in establishing His Church.