Go to menu WooCommerce > Settings
On the General tab, add the new country to the list first. Click the Save Changes button.
Click the Shipping tab
You will see a list of zones. Each zone can have more than 1 shipping method.
Click the Add shipping zone button.

Key in the Zone name.
Select the region from the dropdown list.

Click the Add shipping method button to to start adding new shipping method to this new zone.

You will see a popup like below image.
Choose the shipping method from the dropdown list.
Click the Add shipping method button.

Click Edit to enter the shipping rates.
Once you’re done, click on the Save changes button to save the changes.
