Definitions of establishment:

• noun:   a public or private structure (business or governmental or educational) including buildings and equipment for business or residence
• noun:   the cognitive process of establishing a valid proof
• noun:   any large organization
• noun:   (ecology) the process by which a plant or animal becomes established in a new habitat
• noun:   the act of forming something

  Example: "It was the establishment of his reputation"

• noun:   an organization founded and united for a specific purpose
• noun:   the persons (or committees or departments etc.) who make up a body for the purpose of administering something

  Example: "He quickly became recognized as a member of the establishment"