To establish means to create or set up something, usually an organization or institution. In the context of the question, it refers to the action of creating America's first National Bank.
Related terms
Institution: An institution is an established organization or establishment that serves a particular purpose within society.
Founding: Founding refers to the act of creating or establishing something, typically in reference to organizations or countries.
Charter: A charter is a written document that grants rights and privileges to an organization, such as a bank, outlining its purpose and scope of authority.