He challenged the 'established order'. [=the way things are usually done in society, in an organization, etc.]
Research has 'established' [='demonstrated, shown'] that he played an important role in the negotiations.
Investigators are trying to 'establish' if/whether anyone knew about these problems before the accident.
(..) ...charged with maintaining the defense of the planet Krypton itself. Chief Architect of this intended revolution and author of this insidious plot... ...to establish a new order amongst us... ...with himself as absolute ruler. You have heard the evidence. The decision of the Council Guilty! (..)1978 Superman
(..) your view on this questionnaire, sir. Oh, no, no, no, no. You were doing fine. You had been courteous and receptive to courtesy. You had established trust, with the embarrassing truth about Miggs. And now this ham-handed segue into your questionnaire. - It won't do. (..)1991 The Silence of the Lambs
(..) Every day you come in with your six cents. At the end of the week, you get your sandwich. - Are you gonna be an asshole? - What am I, fuckin' sandwich welfare? I think you should establish a good line of credit. Like how you bought your couch: Payment plans. Remember how your mother brought (..)1997 Good Will Hunting