Origin's Kupe project director Peter Ashford said sporadic flaring might be visible, and possibly even audible, 30km away on the south Taranaki coast.
Testing was expected to take about a week, he said.
Afterwards the Ensco rig will move to drill the nearby Momoho prospect, about 5km from the production facilities in the field's central field area.
Momoho has the potential to contain 100-150 petajoules of gas, although it could also hold oil, and the partners have not assigned any reserves to the prospect.
The Kupe partners are operator Origin Energy (50%), Genesis Energy (31%), New Zealand Oil & Gas (15%), and Mitsui E&P NZ (4%).