What is production under type certificate?
Production under type certificate authorizes the manufacture of a product under the FAA-approved type design for up to 6 months after the type certificate is issued. 

This type of production requires the FAA to increase its level of involvement. Due to limited FAA resources, there may be delays in the FAA's ability to conduct airworthiness inspections and to issue airworthiness approvals. Except as otherwise authorized, the FAA will discontinue its conformity and airworthiness inspections after 6 months from the date the type certificate was issued.

How do I obtain authorization for production under type certificate?
You would obtain production approval (under type certificate) as part of your type certificate. Separate application is not required.

The manufacturer is required to make each manufactured product available to the FAA for an airworthiness inspection. The FAA issues the necessary airworthiness documentation for each manufactured product that conforms to its FAA-approved type design data. The manufacturer is required to maintain, at the place of manufacture, the technical data and drawings necessary for the FAA to make its determination whether the product and its articles conform to the type design.

Production approval regulations & policies