We are looking into changing our current mobile banking platform to a mobile app which is supported by Apple/ Google. Would we have to make changes updating our current Privacy Policy? Looking for guidance on this one.

What privacy disclosure is this going to impact? Would this not just be a service provider?

It might have privacy impacts if the new app vendor collects additional data that the bank doesn't currently collect, and the customer or bank cannot control the collection through a contract or opting out. Think, for example, about location services.