The first course of action when one of the organization's critical third-party providers experiences a data breach is to invoke the incident response plan, which means activating the incident response team and following the predefined procedures and protocols to respond to the breach. Invoking the incident response plan helps to coordinate the communication and collaboration with the third-party provider, assess the scope and impact of the breach, contain and eradicate the threat, recover the affected systems and data, and report and disclose the incident to the relevant stakeholders and authorities.
References = Cybersecurity Incident Response Exercise Guidance - ISACA, Plan for third-party cybersecurity incident management