The phrase "a profound unease" is correct and usable in written English.
It can be used to describe a deep or significant feeling of discomfort or anxiety about a situation or topic.
Example: "As the discussion progressed, a profound unease settled over the room, leaving everyone in silence."
Alternatives: "a deep discomfort" or "a significant anxiety".
But I for one, feel a profound unease at the thought of having a president who proudly proclaims that he does not believe in evolution.
There is, I suggest, cause for a profound unease in the notion that, in the very trial which you face as an accused, your advocate has asked to be assessed.
went up at the Atlanta Falcons game here when the news broke, people in smaller groups and in individual conversations expressed a profound unease about the potential for new terrorist strikes now that the battle had been engaged.
Then comes the revelation of a deeper propellant, a profound unease that began in childhood – Bruce was nicknamed "Blinky" in primary school on account of his fluttering eyelids – and erupted into full-blown depression in his 30s, on the eve of 1984's Born in the USA, the album that brought him global stardom.
"We are in a moment of profound unease about the stability of the executive branch of our government," he began.
The release of a videotape by a man calling himself a military spokesman for Al Qaeda, and the arrest of the three Moroccans, have left Spain's Muslim population in a state of profound unease.
As a signal of the profound unease that his candidacy has generated among senior Republicans, the speaker of the House, Paul Ryan, effectively dumped Trump, telling congressional colleagues that he would neither defend his party's nominee nor campaign with him.
Those who admire some portion of Eisenberg's writing will find the same pleasures in the whole: remarkable language, unconventional storytelling and her characters' well-rendered and profound unease at inhabiting an uneasy world.
In part, it may be because the McCann case speaks to a profound noughties unease about the rules and roles of parenthood.
A strange feeling washed over me last night, and profound unease: I was driving home from the cinema, where I saw the latest James Bond film "Spectre," when I heard the breaking news on the radio, announcing what would become known as "the Paris attacks".
Moments of majestic assertion give way to profound unease as themes splinter and fray.
