Regional lender Citizens Financial Group opened a new private bank for wealthy customers last month. Its inspiration: First Republic Bank, which collapsed earlier this year in the second-largest bank failure in history. 

Citizens, based in Providence, R.I., is spending tens of millions of dollars hiring former First Republic staffers. It hopes the strategy will help it crack a market it has long coveted. Executives say they plan to copy only the good parts of First Republic, such as its beloved customer service.