"To establish a history" means to create or build a record of past events, actions, or information about something or someone.
Sentences with «to establish a history»
This is a simple way to improve your credit by establishing a history of paying on time. (discover.com)
This can also be the same for those with established history, with credit that might be low based on previous expenses and financial struggles. (studentloans.net)
Older accounts even with a zero balance establish your history as a credit user. (privacyrights.org)