“Who gave him the 'authority' to do this?” “He didn't do it 'on his own authority' [=he didn't do it on his own]; he was acting 'under the authority of' the company president.” [=the company president gave him the power to do it]
No one 'in authority' objected to the plan. = No one 'in a position of authority' objected to the plan. [=no one with official power to make important decisions objected to the plan]
This office has 'authority' over personnel matters. [=this office has the power to make decisions about personnel matters]
(..) Let justice be done upon him! My master, Sauron the Great, bids thee welcome. Is there any in this rout with authority to treat with me? We do not come to treat with Sauron... ...faithless and accursed. Tell your master this: The armies of Mordor must disband. He is to depart these lands, (..)2003 The Lord of the Rings: The Return of the King
(..) of this Aragorn, son of Arathorn. And I tell you now, I will not bow to this Ranger from the North... ...last of a ragged house long bereft of lordship. Authority is not given to you to deny the return of the king, steward. The rule of Gondor is mine and no other's. Come. (..)2003 The Lord of the Rings: The Return of the King