How do changes in certification requirements affect previous type certificates?
New rules don't affect t existing designs.... 

Certification basis is declared by the maker and agreed with the certifying authority...Or authorities... ( ideally it's a common certification basis to avoid extra testing, or building aircraft to  different standards) That basis must reflective rules in existence at the time of application. New or pending  rules may be imposed by Special Conditions or equivaent. Any modifications to that approved design are normally to the same certification basis. 

But if a new design comes along, it's the applicable rules at the time of application.. 

If a change is needed to all aircraft of a certain "class" e.g. Introduction of TCAS, ACAS , then that is imposed by operational requirements, such as Parts 91, 121, 135 etc or their equivalents.