"dominant authority" is correct and usable in written English.
You can use it when you want to refer to a powerful or influential leader or institution that has a lot of control or influence over others. For example, "The dominant authority in this country is the monarchy, and all citizens must obey its laws."
The All England Club was the dominant authority then, the British Lawn Tennis Association LTAA) not being formed until 1888.
Individuals cannot have such aims, much less such "rights," until the dominant authority of custom or hierarchical privilege has been swept away.
This influence is usually regarded as a negative force because it refers to a process through which cultural identities and practices of a dominant authority (such as a particularly powerful state, city authority, or ethnic group) are reinforced by undermining the existence of other, less-powerful identities.
The palate, not the intellect or the soul, has become the dominant authority.
Before long, Thomas's thinking on this point became the dominant authority in Christian doctrine.
Gin's the dominant authority figure through most of the film, until Lois crushes him to death with the getaway van.
Even so, Rangers have not progressed with style as they have made their way through the divisions and the support yearns for a dominant, swashbuckling authority.
Contrary to years past, one dominant religious authority (Christianity, and more specifically Protestantism) no longer holds all the cards and makes all the rules.
Dajani observed that the current bid for UN recognition highlights a crucial tension between these visions, and he distinguished between the dominant Palestinian authorities, whose maneuverings to win statehood have "sacrificed the vibrancy of the [PLO] movement," and a younger cohort seeking to shift the discussion to human rights.
"When you're in power, and want to stay there, you are not free to be yourself; you are expected to live up to your role as a dominant decisive, absolute authority — and to internalize it, to drink your own Kool-Aid," said Jennifer Overbeck, a psychologist at the University of Southern California.
The nations on the sock symbolised unity after the World Cup's 12-year hiatus following World War II and it gave a nod to the previous World Cup poster at France 1938, which saw a blank dominant figure expressing authority in a similar pose with a boot over the world.
