Following the destruction of the original Namek by Frieza, the revived Namekians were forced to spend an entire year on Earth inside the Capsule Corporation compound with Bulma and the Briefs. Eventually, King Kai discovered a planet with an atmosphere identical to that of Namek, and thus the Namekians were wished to that planet after bidding farewell to their friends from Earth.
New Namek is mentioned and seen in the Cell Games Saga, Dragon Ball Z: The Return of Cooler, Kid Buu Saga, Baby Saga, and Shadow Dragon Saga. During the Cell Games Saga, Goku travels to New Namek using Instant Transmission in order to find a replacement Guardian for Earth. Dende is selected, and happily accompanies Goku back to Earth.
During the events of Dragon Ball Z: Resurrection ‘F’, New Namek was also mentioned by Sorbet when he and his men that they were trying to find the planet in order to use the Namekian Dragon Balls to resurrect Frieza, but couldn't locate it even with the help of the spy robots. In disgust, he orders them to stop searching after failing to locate the planet so Sorbet and his aide, Tagoma decided to go to Earth instead. This inadvertently spared the Namekians of having their planet invaded by the surviving remnants of Frieza Force lead by Sorbet.
In Dragon Ball Super, Old Kai and Kibito Kai retrieve the Namekians' Dragon Balls as they thought Champa was after them but he wasn't. Kibito Kai uses the Dragon Balls to reverse the Potara Fusion of the Supreme Kai and Kibito. In episode 63, Goku Black and Future Zamasu clearly said they destroy all of the dragon balls and they destroy all of the mortals, implying that New Namek is likely destroyed in Future Trunks timeline.
In Dragon Ball Z: The Legacy of Goku II, right before the Cell Games, the Z Fighters accompany missing Namekians back to New Namek. They get Grandpa Gohan's key from one of those Namekians who found it in the woods near Goku's house. In a cave there, the Z Fighters confront and defeat Cooler in his fifth form.
New Namek appears briefly in the Story Mode of Dragon Ball Z: Supersonic Warriors 2 and Dragon Ball Z: Shin Budokai - Another Road. In the latter, Future Babidi goes off to New Namek to use the Namekian Dragon Balls to place Buu under his control. Future Cooler and Future Broly join forces and help Future Babidi. The Z Fighters fight with them on New Namek, and later bring Future Dende to Earth to become the new Guardian have Dragon Balls on Earth again.
According to Dragon Ball Online, Mira attacks New Namek in Age 851 and eventually destroys it in Age 853 with a Spirit Bomb. Thus, the Namekians lead by Grand Elder Moori are forced to relocate to Earth, where they remain.
In Dragon Ball Xenoverse 2, Towa uses a Wormhole to connect Earth in Age 767 of the main timeline to New Namek in Metal Cooler's timeline causing Metal Coolers that had been invaded New Namek to appear at the Cell Games. Chronoa orders Xeno Trunks to travel to New Namek to deal with the Metal Cooler's on New Namek while the 2nd Future Warrior deals with the Metal Coolers that have come through the wormhole before using the Wormhole to travel to New Namek to aid Xeno Trunks and prevent more Metal Cooler's from traveling through. Xeno Trunks uses his technological skills to program the Big Gete Star's central computer to self-destruct in order to kill Metal Cooler Core and cause a chain reaction to destroy the remaining Metal Coolers. Eventually the Big Gete Star self-destructs and the Metal Coolers are destroyed. Xeno Trunks destroys the Wormhole and peace presumably returns to New Namek. New Namek is represented in Xenoverse 2 by the Namek stage.