a bank that offers personal services in managing investments and assets to individuals and families with a lot of money 私人银行,私营银行(为富豪提供资产管理服务的银行)
a bank that is not a member of a clearing house (= a central office through which banks pay each other money and exchange cheques) 私人银行,私营银行(非票据交易所成员的银行)
a bank that is not owned by the state 私人银行,私营银行(非国家拥有的银行)