The India side
In India the rent is income from house property, taxed after a flat 30% standard deduction under Section 24, which you get whatever you actually spent, and after home-loan interest, at slab rates. As a non-resident landlord, your tenant must deduct TDS under Section 195 on the gross rent, from the first rupee with no monthly threshold, which over-deducts against your real Indian tax. You recover the excess by filing an Indian return, or reduce it up front with a lower-deduction certificate. India taxes the rent whatever New Zealand does.
New Zealand, and the four-year window
New Zealand taxes a resident on worldwide income, so the Indian rent is assessable there, computed on NZ rules, actual expenses rather than India's flat 30%, and NZ gives a foreign tax credit for the India tax, up to the NZ tax on that rent.
But the timing matters enormously for a recent migrant. New Zealand gives a new tax resident a transitional-resident exemption for roughly the first four years, during which most foreign income, including your Indian rent, is exempt from NZ tax altogether. So in those years only India taxes the rent, and there is no NZ tax on it. One consequence to note: because NZ is not taxing the rent in that window, there is no NZ tax for the India tax to be credited against, so the India tax stands alone and is recovered, if over-deducted, only through your Indian return. After the four years, NZ taxes the rent with a credit for the India tax, and if the Indian property runs at a loss for NZ purposes, that residential loss is ring-fenced, it cannot be set against your NZ salary or other income.