"great independence" is correct and usable in written English.
You can use it when discussing freedom and autonomy. For example, "My parents gave me great independence from a young age, which I'm very grateful for today."
Some states allow the testator (maker of a will) to give the executor great independence to act with minimal judicial supervision (independent administration).
Shortly thereafter, Berengar, who always exhibited great independence of thought, began to teach ideas contrary to prevailing beliefs.
In the early post-communist years, the trend was to give judges great independence but low salaries.
The judges, who are appointed by the President and serve for life, enjoy great independence and generally serve with distinction and honor.
They divided up power between the mayor and a city council, and they also gave great independence to agencies such as the police.
The counts of Provence allowed the city great independence, and only in 1245 and 1256 did Charles of Anjou force acknowledgement of his sovereignty.
The title references Salman Rushdie's great Independence-themed novel, Midnight's Children, about a sampling of characters all born at midnight on August 15 , 1947 the moment India became a free country.
She has been almost ostentatiously independent of the president, but her greater independence is a matter of public attitude only.
Board Diversity: Greater independence doesn't always drive greater diversity.
Greater independence of non-executive board directors is certainly desirable.
That means, above all, greater independence for schools.
