If you are testing rates at checkout, and you add a new rate to the app, you may need to bust the shipping cache to tell Shopify to pull in new rates.
Shopify employs a shipping cache. This means that when rates are retrieved for the specific combination of Products in Cart & Shipping Address, Shopify will cache the returned rates on their servers for a day or so. If the exact same combination of products/address is tried again, any changes that have been made to shipping rates will not show.
When testing, it's common to run a checkout, change some rates, and simply refresh the checkout. This will now show the new rates!
How to bust the cache:
Increment the street number of the address each time you test a rate.
Try a completely different address
Add different products to the cart
Read more about busting the shipping cache.