An application can be made by a de facto partner.

Regarding the application Form A, the definition of a "near relative" in the Regulations is
"a) the spouse, civil union partner, or de facto partner of the deceased, but only if that person was living together with the deceased immediately before the death; and
b) a parent of the deceased; and
c) any child of the deceased who is aged 16 years or over; and
d) any other relative of the deceased who usually resided with him or her

In New Zealand, the legal definition of a de facto relationship is complex. The standard legal definition of "de facto" includes that the couple live together.
A de facto relationship may be deemed to end when the partners live apart.
One guideline is that the couple must have been living together for three years but that is not absolute.

There is an issue when one de facto partner has to move to a separate care facility before the death.
According to the Cremation Regulations, if the partner then dies in the care facility, the surviving de facto partner was not a "near relative" for the purposes of the application.
It is a tricky issue because that definition (living together "immediately before the death") also applies to legally married partners and civil union partners.

This is not an issue if the surviving partner is an executor.

If there is no executor, it is helpful to specify how long the partners have lived apart before the death. If it was months or years then it would be preferable to have the application made by another "near relative."