Budget 2019 is out and Vote Prime Minister and Cabinet reveals taxpayers spend $10m per year on our de facto head of state, the Governor-General. That’s about the same as an actual head of state.

Governor-General's Programme PLA (M52)
This appropriation is limited to expenses incurred on the Governor-General's Programme, as authorised by section 13 of the Governor-General Act 2010. $1,500,000
Governor-General's Salary and Allowance PLA (M52)
This appropriation is limited to expenses incurred on the salary, allowance and other payments to the Governor-General, as authorised by section 12 of the Governor-General Act 2010. $500,000
Governor-General's Travel Outside New Zealand PLA (M52)
This appropriation is limited to expenses incurred on the Governor-General's travel outside New Zealand, as authorised by section 14 of the Governor-General Act 2010. $407,000
Government House Buildings and Assets MCA (M52)
The single overarching purpose of this appropriation is maintaining the Government House buildings and related assets in Wellington and Auckland to the standards necessary to fulfil their constitutional, ceremonial and community roles. $3,322,000
Support Services to the Governor-General and Maintenance of the Official Residences
This category is limited to financial, administrative, communications and advisory services for the Governor-General; and services to maintain the Governor-General's residences. $4,179,000

Total is $9,908,000

In contrast, the President of the Republic of Ireland spends (according to their 2019 budget) €4.5 million, which is $8.7m in New Zealand dollars - so about the same.