I outsource IT service and data storage. Do I still have cyber risk?

You have probably done a great job choosing partners for IT services and data hosting.  You may even have ensured that your contracts within those providers included language to protect you in the case of a breach.  Unfortunately, you are still entirely responsible for the impact a breach of your chosen systems has on your customers, vendors, and other stakeholders.  The only reliable way to outsource this risk is through cyber insurance.