Hey @Roanne,
In order to connect or make changes and updates to an integration, you must have at least Manager level permissions within Klaviyo as detailed in the Guide to User Management and Privileges Help Center article. As far as the permissions on the integration side of things, we typically recommend either being the account owner or having at least admin level access which are granted integration permissions.
That error suggest that a potential resolution would be to fully remove the Shopify integration and attempting to full re-integrate Shopify with Klaviyo again. In the event your Klaviyo account already has a Shopify integration set, you can attempt to fully remove the integration per the Disable or Remove a Klaviyo-Built Integration article and attempt a full re-integration of the Shopify instance per the How to Integrate with Shopify guide.
If this issue persists, I would suggest reaching out to our Klaviyo support to take a look further into your accounts integration or alternatively reaching out to Shopify Support for more details in your account and potential causes preventing you from updating the integration settings between these two platforms.
David