We are GDPR compliant and have the ISO 27001 certification. We have just terminated an agreement with a data processor. Do we legally need to inform our clients and customer that we have terminated that data sub processor agreement?
This depends whether or not you are a controller or a processor. If you are a processor and want to change one of your sub processors you will need to at least notify the respective data controllers about the change. If you are a controller you don't need to inform the data subjects about such a change.