The phrase "layer of authority" is correct and usable in written English.
You can use it to refer to a hierarchical structure of authority, where one person or entity has authority over those beneath them in the hierarchy. For example, "In a large company, there are distinct layers of authority, starting with the CEO and making their way down to entry-level employees."
Healthy companies tend to resist, for fear of setting off power struggles or imposing a disruptive new layer of authority.
Chris Wendelken, seated in the middle, wears dark red lipstick, applied Joker-style (and we briefly see on the screen an image of Heath Ledger as that villain), and seems to have an added, if tenuous, layer of authority.
He has added a new layer of authority at the top, taken command of numerous committees, and now personally supervises overall government reform, finance, the overhaul of the armed forces and cyber-security.
One of the "quorum of 70" (the next layer of authority after the apostles) is Japanese and another British.Wherever it goes, the faith retains a Middle Western flavour, with its mixture of social conservatism, philanthropy, worldly shrewdness and devotion to a core set of beliefs.
They're backed by McCartney's band, which ostensibly adds another layer of authority.
HypeMachine is integrated seamlessly with Soundcloud, giving Soundcloud, land of terrible GarageBand DJs, a layer of authority it does not yet have on its own.
A multiplex world would have multiple layers of authority and leadership.
At a huge bank like JPMorgan, there are many layers of authority, and nobody knows everything that is going on.
He chafed at the family-style layers of authority when he won two Super Bowls with the Giants.
Others like Lynette McElhaney, a city councilwoman, were more skeptical, saying that the increasing layers of authority would sow confusion.
Clinton, while en route to Haiti, took note of the layers of authority in Haiti, which include the Brazilian-led U.N. security force.
