On Tuesday we have a weak area of low pressure lying over the North Island in the morning which weakens further in the afternoon, while over the South Island we see an area of low pressure start to form.

In the North Island, areas of cloud dominate for almost the whole northern half of the island, with light winds for most then afternoon onshore winds.
Isolated showers are possible from the afternoon and evening, all the way from Northland down through to Taranaki, and across to the ranges of Hawkes Bay and Gisborne.
Showers once again are quite isolated, so many may remain fairly dry.
Winds change to gusty southerlies in Wellington later in the evening, bringing cloud and the chance of a shower there too.

Over the South Island we see areas of cloud on the West Coast, before breaking away during the afternoon, with southwest winds.
Along the east coast we see mostly sunny weather with light winds, and southerlies work into the lower South Island by midday – bringing cloudy areas and the chance of a light shower or two.
Southerlies hit Canterbury at some point late in the afternoon or early evening, then into Marlborough by mid evening. 
Canterbury sees the chance of drizzle as southerlies hit then the risk of showers goes up in the evening – especially inland before clearing away overnight.

– Aaron Wilkinson & Drew Chappell, WeatherWatch.co.nz