The most recent incarnation of a national chess magazine has been New Zealand Chess which began publication in 1975 but is sadly due to cease publication in 2018. Interest in the magazine has waned as audience tastes have swung increasingly towards more immediate and up to date chess news. Improvements in the NZCF website itself should pick up the slack from 2019.
Note that the dedicated New Zealand Chess website includes almost all recent magazine content in online play-through format, a feature that is rumoured to have accelerated the demise of the magazine itself.
All issues from recent years, and an increasing number of older issues are now available in viewable PDF form here. The intention is to provide a complete collection soon.