New Delhi, Sept. 17 -- Indian-born bankers have led global financial giants from Deutsche Bank AG and Citigroup Inc. to Barclays Plc. Yet at home, the country's lenders can face a string of challenges finding executives for the top job.

The subject of succession has been in sharp focus with India's largest private bank-HDFC Bank Ltd.-hunting for a new chief executive officer after its current boss decided against seeking an extension. Another financial heavyweight, Kotak Mahindra Bank Ltd., is on its second CEO search in three years. Neither had a clear successor waiting in the wings, setting the stage for a complex hunt.

Private-sector banks looking for potential C-suite talent are often circling the same pool of candidates in India, w...