Your constraints are pretty strict. There aren't many places which could be settled (in recorded history) where there weren't already people living there, and where there was a reason for not continuing contact with the place of origin.
Another possibility is Te Pito O Te Kainga / Rapa Nui / Easter Island. The first explorers met one person already there (Nga Tavake), then they go back to Hiva, and a double canoe returns to Easter Island carrying the settlers. They left "because a rising tide was destroying their land" and/or a power struggle with the Hanau Eepe, if I read http://archive.hokulea.com/rapanui/hotu.html correctly. In either case, the oral history suggest little continued connection with Hiva.
There were 18 years between the European settlement of Pitcairn island and the next visitors - https://en.wikipedia.org/wiki/Pitcairn_Islands#European_sett... .
Your constraints are pretty strict. There aren't many places which could be settled (in recorded history) where there weren't already people living there, and where there was a reason for not continuing contact with the place of origin.
Another possibility is Te Pito O Te Kainga / Rapa Nui / Easter Island. The first explorers met one person already there (Nga Tavake), then they go back to Hiva, and a double canoe returns to Easter Island carrying the settlers. They left "because a rising tide was destroying their land" and/or a power struggle with the Hanau Eepe, if I read http://archive.hokulea.com/rapanui/hotu.html correctly. In either case, the oral history suggest little continued connection with Hiva.