“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]
(..) Well, I'll leave you to get settled. Sorry, ma'am. Can't let you pass. Let her in. On my authority. She has a right to anything behind that door. That's a nice one. The colors are lovely, of course. (..)2015 The Hunger Games: Mockingjay - Part 2