You Do Need power plug adapter while traveling from New Zealand to São Tomé and Príncipe.

Here is Why You Need An Adapter

The outlet and plug type used in São Tomé and Príncipe are C and F and in New Zealand is I. This is how they look like.

New Zealand

In New Zealand, outlets of type I are in use.

Type I

São Tomé and Príncipe

In São Tomé and Príncipe, outlets of type C and F are in use.

Type C

Type F