Where you start from is your existing products, customers and core competencies to deliver.
Customer contact points need to be reinvented. Role of digital channel has to be enforced. In normal situation there is always conflict between old and new channels. You need to figure out how to safe guard the existing channels and still grow new channel in harmony.
Customer needs are changing too. The way customer uses product or what they need from it might have changed radically. Is your product still relevant? If not, you should figure out what features still create value for customers and reinvent it accordingly. Or in more radical case, do you have what it takes to completely transfer your products into new domain?
Core competences that are needed to produce your service will evolve over time. Do you have capabilities that are needed in current situation or have you focused your capabilities to historical needs? Often combination of old and new capabilities is good thing to have. You just need to be aware when is right time to shift the balance forward.
Organisation is usually hopefully reflecting the priorities of company. New situation demands readiness to reconfigure responsibilities in order to be able to fulfill the emerging needs. Competences within organization are not effectively available, if the structure is blocking the utilization of them. Silos are typical symptom of this. Capability to cooperate is the key here.
You cannot just reinvent product for digital age, your need to reinvent your business completely and fine tune all parts of it to be fit for the new breed of customer expectations.