To use the new date selector, in Setup, create a task update action or edit an existing action. Prepend “Defer” to the contents of the Name field (then save the action and add it to a task layout).
For example, suppose you have an action with the label “Sales Task” and the name “Sales_Task”. Insert “Defer” at the beginning of the name.
For more information, see “Create Object-Specific Actions” and “Customize Actions with the Action Layout Editor” in the Salesforce Help.