'an air of authority' is correct and usable in written English. It is a phrase that describes the manner in which someone conveys that they have authority or control over a situation. For example, "Samantha spoke with an air of authority about the situation."
"They universally project an air of authority".
His soft baritone possesses an air of authority.
Though they are there unofficially, they carry an air of authority that can discourage any trouble.
The military presence can also bring an air of authority that might elude more conventional stunts.
Mr. Pink was slender and graying, and had an air of authority about him.
Buy from Amazon.com, Amazon.co.ukDOCTORS like to project an air of authority when making their clinical decisions.
His presence lent an air of authority, and we were promptly waved through.
Science therefore steps in with an air of authority and sets him right.
She is une grande femme, a distinguished woman with an air of authority – and nice shoulders.
There was an option to download credentials to lend an air of authority.
He radiates an air of authority, dressed in a blue blazer.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union