The chief operating officer, who joined from Etiqa in 2019, takes charge on 1 October after running the insurer's bancassurance and financial adviser channels.
The Singapore-based executive brings more than 14 years of underwriting and management experience across the energy and chemicals sectors to the expanded role.
The appointment marks Ishida's return to AIG after more than a decade, following leadership roles at Everest Insurance, Zurich and other global insurers.
The leadership change follows Markel's broader Asia-Pacific expansion strategy, including ambitions to nearly double its regional business over the next five years.