I think the Australian Navy was sending some ships with supplies. They are good at this sort of stuff, bring in water purifiers, build some temp housing, rebuild roads and other facilities.
I presume the only comms are via satellite phones. Internet would be tricky, not sure if they have any satellite systems and where those would link to (geostationary probably visible from Auckland NZ)
Starlink wouldn't help, needs a local link station which would also suffer from the outage. Yeah Starlink is really just a local relay via satellites.