First, users must have Advanced Shopify or Shopify Plus plans or yearly billing. See link:
Third-party carrier-calculated shipping rates
Second you need to have set up your Shipping Zones
You also need to have completed a test order.
Also check out these links to set up backup rates. Learn more about backup rates in the Shopify Help Center, or customize backup rates in your Shopify Admin.
1. Click “Orders”
2. Click “Enable live shipping rates”
3. Scroll down and make sure you are in “Production environment”
4. Click “Save”
5. Click “Settings”
6. Click “Shipping and delivery”
7. Click “General Shipping Rates”
8. Find the Turn 14 Distribution API shipping zone and click “add rate”
9. Click rate type and select “use carrier or app to calculate rates”
10. Select the “Turn 14 distribution API (rates provided by app)”
11. Click “Done”
12. Scroll down and click “Save”
*Please note a phone number is required in the address section of the checkout.
Here is an example of live shipping rates at checkout: