“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]
(..) in front of the other lords and ladies, you undermine me. - So I can't question your decisions anymore? - Of course you can, but... Joffrey never let anyone question his authority. You think he was a good king? Do you think I'm Joffrey? You're as far from Joffrey as anyone I've ever met. Thank you. (..)2017 TvShow: Game of Thrones Title: Dragonstone Season: 7 Episode 1