You Do Need power plug adapter while traveling from Saint Helena to Pitcairn Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Pitcairn Islands is I and in Saint Helena is G. This is how they look like.

Saint Helena

In Saint Helena, outlets of type G are in use.

Type G

Pitcairn Islands

In Pitcairn Islands, outlets of type I are in use.

Type I