The phrase "assert their place" is correct and usable in written English.
It can be used when discussing the act of claiming or establishing one's position or role in a particular context or environment.
Example: "In the meeting, she confidently asserted her place as the project leader, ensuring everyone understood her vision."
Alternatives: "claim their position" or "establish their role."
Cemeteries, funerals, the legacies and possessions of the dead are featured prominently in Mr. Cox's pictorial scheme, not to eclipse the living but to assert their place in the continuum.
Young men once headed to the Ivy League to acquire the patina of high culture that would allow them to move in the circles of power — or if they were to the manner born, to assert their place at the top of the social heap by flashing what they already knew.
Early on, the mothers started calling themselves the Dream Makers, as if asserting their place as the true producers of the boys.
IN one great wave a few years ago, Greek restaurants seemed to wash over Manhattan, coming to rest in almost every neighborhood and asserting their place in the mid-90's vogue for Mediterranean food.
And for Mr. Allen, the phase of his career that began with the 2005 release of "Match Point" has seen him delve into female characters who are further removed from his familiar life experiences, and more interested in finding and asserting their place in the world.
A concept inaugurated in 1951 by New York's Museum of Modern Art, with its show 8 Automobiles, car-centric exhibitions have long since asserted their place in temples to aesthetics.
In short, only humans are free and they only attain freedom through moral agency, by asserting their place in the human realm.
I think some of it also has to do with stigma and this younger generation wanting to blend in with the mainstream more both in terms of kind of asserting their place in the mainstream.
The life it depicted — in which black men called white men "boss" and white men called black men "boy"— began to recede as African-Americans asserted their rightful place in American society, as the black middle class began to grow, and as black accomplishment became an ordinary part of American life rather than something unique.
As Americans debated the relative relevance of race and gender to politics, African American women asserted their unique place at the crossroads of the question.
The book's real strength lies in its analysis of the post-Civil War era, when a flood of new money forced New York's more established families to look to the public arena as a place to assert their distinctiveness.
