"gradually establish" is correct and usable in written English.
This phrase is typically used when introducing an idea or action which will happen over a period of time. For example: "We will gradually establish a new policy to reduce our emissions."
As their families become less Japanese and more American, the women gradually establish a new equilibrium, only to have it shattered in a passage, simply called "Traitors," that returns to the forced removals of World War II.
Smith believes that there is a way in which rational modes of thought gradually establish themselves in the popular mind, and to this extent he thinks that there is something in the idea that modernity brings a kind of secularisation - what Max Weber, one of the founders of modern sociology, called the "disenchantment of the world".
China's plan appears to be to gradually establish a de facto presence in the waters, and now the airspace, around the disputed islands.
Thus, a universal proportional carbon tax should be considered as the ultimate solution, and an enabling political arena is needed to gradually establish the system.
Through such procedures, the Chinese leadership, academia, and the public could gradually establish a reflexive system toward "nation/minzu" issues, knowing the peculiarities of these issues and their universalities we share with other countries.
Encode that in your memory, and take notice of how your body and thoughts gradually establish their fragile equilibrium.
Tai kingdoms were gradually established farther and farther south.
It gradually established a literary, philosophical and theatrical identity all of its own.
So he honed his tutoring skill at Princeton Review and gradually established an independent practice in Westchester.
Since then, his newspaper articles and TV appearances have gradually established him as a media celebrity.
A director of personnel was employed who gradually established rapport with the employees.
