When setting up Easyship Rates in your Shopify store, there are some settings that need to be added.
Provided that you have 3rd Party Calculated Rates enabled on your Shopify store and connected your Easyship account with your store.
You will also need to add Easyship to your Shipping Zones.
When logged into Shopify, at the bottom left you have Settings, please click it. Once in settings you go to SHIPPING.
In the above example, the store only allows shipping to anywhere in the United States, and its always for free. Shipping to the rest of the world is not enabled.
To add Easyship Rates, press Edit on the shipping Zone you wish to add it to.
At the bottom of the next page, you have Calculated Rates.
Click Add Rate.
Once here, you should be able to select Easyship (Rates provided by app) provided everything has been correctly installed and you have 3rd Party Calculated rates enabled by Shopify.
Once selected and additional options have been set to your liking, press save and the Easyship rates should now be visible in the shipping zones page as per below.
In the above selection, we now can see that we have Easyship rates provided to the "Rest of the World" while the US only has Free Shipping as an option.
To read up more on the settings you can do in Shopify Shipping Zones, please have a look at Shopifys Helpcenter located here: https://help.shopify.com/en/manual/shipping/zones