To restrict playbook execution to members of the admin role within Splunk SOAR, the 'Execute Playbook' capability must be managed appropriately. This is done by ensuring that this capability is removed from all other roles except the admin role. Role-based access control (RBAC) in Splunk SOAR allows for granular permissions, which means you can configure which roles have the ability to execute playbooks, and by restricting this capability, you can control which users are able to initiate playbook runs.