2. well before, well in advance, a long time prior - when noa atu follows mua it indicates that something happened a long time prior to some other event.
He kupu tawhito tonu anō a 'Māori', nō mua noa atu i te Pākehā nei (JPS 1894:30). / 'Māori' is quite an ancient word, from well before the Pākehā arrived.
3. long after, well after, a long way away - when noa atu follows muri, or another word of time or place, it indicates that something happened a long time after some other event, or was some distance away.
Ka haria ngā papa me ngā haeana hei hanga whare karakia anō mōna ki Otamaoa. Ka whakatūria ki muri noa atu i tō mātau whare (EM 2002:55). / The timber and iron was taken to build another church for him at Otamaoa. It was erected a long way away from our house.
Kua whakahokia e koe te ingoa nei, me Māui ki muri noa atu o Wahieroa, o Whaitiri, i a Hāpai- ariki, i a Tupuaterangi. E Tuhi, e hē rawa ana tēnei. Ēnei tāngata kei muri noa atu o te waipuke (TTT 1/11/1929:1915). / You have placed this name with Māui long after Wahieroa, Whaitiri, Hāpai-ariki and Tupuate rangi. Tuhi, this is absolutely wrong. These people are long after the flood.
4. much more - when following an adjective noa atu can indicate comparison.
Nō tētahi tangata nui noa atu tōu hāte. / Your shirt belongs to someone much bigger.