To meet the requirement of granting Read/Write access to child Opportunities for Account Team members with the Executive Sponsor role, an Opportunity sharing rule should be created. Sharing rules in Salesforce allow you to automatically extend access to users based on their roles or other criteria. In this case, the sharing rule would be configured to provide Read/Write access to Opportunities for those in the Executive Sponsor role on the Account Team.
Reference:
Sharing Rules Overview
Create and Edit Sharing Rules