You Do Need power plug adapter while traveling from Tanzania to Zambia.

Here is Why You Need An Adapter

The outlet and plug type used in Zambia are C, D and G and in Tanzania are D and G. This is how they look like.

Tanzania

In Tanzania, outlets of type D and G are in use.

Type D

Type G

Zambia

In Zambia, outlets of type C, D and G are in use.

Type C

Type D

Type G