New Delhi, Aug. 31 -- For over three decades, Sashidhar Jagdishan was the HDFC Bank insider who rose through the ranks to inherit its most coveted seat. He joined the bank in 1996, spent years running its finance function, and eventually became the man chosen to follow the formidable first chief executive Aditya Puri.

Now, six years after taking charge, 'Sashi', as colleagues know him-and as some of the bank's older annual reports call him-is preparing to leave the corner office at a moment when questions around governance have become as important to the bank's future as growth.

A Mumbaikar, Jagdishan was born and brought up in the bustling bylanes of Matunga, and continues to live in the city with his wife and son. Away from the number...