In your Shift4Shop Online Store Manager, you will find a series of Shipping Settings that can be found by going to Settings > Shipping and then clicking on the Enter Settings button under the "Carrier Settings" section.
Once there, click on the + Icon next to "Shipping Settings to reveal a series of checkboxes. Within this area, you will see a checkbox titled "Hide Shipping Preview,"
Your Shift4Shop store, by default, will have a shipping cost preview added to the store's "View Cart" page. When available, the Shipping Preview function will be listed on your store directly below the Apply Coupon field. When your shopper adds their U.S. Based Zip Code into the field, a quick calculation will be made. Marking the "Hide Shipping Preview" checkbox will remove the option from your store's View Cart Page.
This preview option is useful in that it gives your shoppers a quick estimate of how much their order will cost to ship before proceeding to the full checkout pages. However, if you'd like to remove the option, mark the checkbox and save your changes.