King George V died in January 1936. The new king, Edward VIII, decided that the Dominions would henceforth be allowed to use the uncrowned effigy on their coinage, if they so chose. The Dominions considered that they were equals of Britain, even though Britain was first among equals, and that therefore they should not have to use the crowned effigy as the mere colonies were required to do. The crowned / uncrowned effigy had unexpectedly become an issue of status and to an extent, race: Dominions (ruled by people of British and European descent) versus the colonies.
Edward VIII abdicated in December 1936, and no coins bearing his portrait were issued in the UK, New Zealand or anywhere else, though British patterns do of course exist. King George VI, however, decided to implement Edward's policy of allowing the Dominions to use the uncrowned effigy.
Below you see Humphrey Paget's famous portrait of King George VI, as it appeared on the obverse of a New Zealand florin of 1937.