The phrase "great distrust" is correct and usable in written English.
It can be used to express a significant level of skepticism or lack of trust towards someone or something.
Example: "The recent events have led to great distrust among the community regarding the government's intentions."
Alternatives: "deep mistrust" or "significant skepticism."
Gary Allen's writings conveyed great distrust of the established order.
The roumis in the street were eying us with great distrust.
Whenever there is a great distrust or antipathy, it spills beyond religion into public life," the professor said.
"How will change come in the next 20 years when there's such a great distrust of politicians, even despair at them," he asks.
Of lasting significance was the conviction and hanging of rebel leader Louis Riel, which angered French Canadians and caused great distrust between Francophones and Anglophones across much of Canada.
And the killer — it's better if he comes and says hello than if he flees, because it creates a climate of great distrust when a killer avoids a survivor and won't greet him.
Presumably, there was far greater distrust among the people who refused to take the survey.
But even as residents here view the militants with fear, most express greater distrust of the American forces.
He takes over from Benigno Aquino, whose time in office saw significant economic growth but failed to significantly reduce inequality, leading to a greater distrust of the political class.
But by far the greatest distrust, and the hardest to overcome, is that felt by a sizeable number of Thais, inside and outside the red shirts, towards the country's royalist elite and its political, military and business allies.
With every day of violence, each leader is expressing greater distrust of the other side, and both sides are reverting to the negative dynamic of their old, familiar roles as enemies.
