In re: AD (Tuvalu)

A family from Tuvalu, one of the lowest-lying nations in the world, brought an appeal against a decision to deny them New Zealand resident visas. One of the arguments made was that their home of Tuvalu was threatened due to climate change. The court ultimately granted them immigration status for reasons other than climate change.

http://climatecasechart.com/non-us-case/in-re-ad-tuvalu/

https://climate-laws.org/geographies/new-zealand/litigation_cases/in-re-ad-tuvalu-immigration-and-protection-tribunal-new-zealand-2014