The most common and most likely answer to this crossword clue is the 10 letter word DOMINATION
I've seen this crossword clue in Financial Times
D
O
M
I
N
A
T
I
O
N
Buddy explains!

The straight part
We know that "authority" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case authority = domination.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does DOMINATION mean?
DOMINATION noun- A lid.
- Area or situation which screens a person or thing from view.
- The front and back of a book, magazine, CD package, etc.
- The top sheet of a bed.
- A cloth, usually fitted, placed over an item such as a car or sofa to protect it from dust, rain, etc. when not in use.
- A cover charge.
- A setting at a restaurant table or formal dinner.
- A new performance or rerecording of a previously recorded song; a cover version; a cover song.
- A fielding position on the off side, between point and mid off, about 30° forward of square; a fielder in this position.
- A set (more often known as a family) of sets, whose union contains the given set.
- An envelope complete with stamps and postmarks etc.
- A solid object, including terrain, that provides protection from enemy fire.
- In commercial law, a buyer’s purchase on the open market of goods similar or identical to the goods contracted for after a seller has breached a contract of sale by failure to deliver the goods contracted for.
- An insurance contract; coverage by an insurance contract.
- A persona maintained by a spy or undercover operative; cover story.
- A swindler's confederate.
- The portion of a slate, tile, or shingle that is hidden by the overlap of the course above.
- In a steam engine, the lap of a slide valve.
- The distance between reinforcing steel and the exterior of concrete.
- The act of dominating; the exercise of power when ruling
- A ruling party; a party in power.
- A high order of angels in the celestial hierarchy.
- A fetish characterized by control/power over and discipline of one's sexual partner.