"assert his position" is a correct and commonly used phrase in written English.
It means to state or declare one's beliefs or opinions strongly and confidently. Example: The CEO of the company asserted his position on the controversial issue, firmly stating that the company would not make any changes to its policies.
A lingering personnel question gave Mr. Kelly a chance to assert his position at the top of the West Wing.
Rooney has not been afraid to assert his position in the face of his manager's opinions – it was he who insisted, presciently as it has turned out, that he would be better deployed through the middle – and Ferguson's frustrations about England appear to have fallen on deaf ears in a World Cup year.
Mr Murphy needs to unite the party and assert his position, in the wake of comments by his leadership predecessor Johann Lamont that Scottish Labour was treated like a "branch office" by Westminster colleagues.
His live performance at this years Parklife looks set to assert his position within a new generation of producers; one whose experimentations with house, techno and electronica have captured the imaginations of so many.
One Hollywood manager routinely asserts his position while assessing another's place in the pecking order by asking where the other person lives.
By the death of George Frederick of Prussia, Joachim became regent of the duchy of Prussia, ruled nominally by the mentally retarded Albert Frederick, but he had some difficulty in asserting his position (the position being established more firmly by his son and heir John Sigismund, who eventually became duke of Prussia).
Darius asserted his position as king by force, taking his armies throughout the empire, suppressing each revolt individually.
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He endlessly asserted his positioning as a champion of job creation and saving the middle class without discussing policies that would do that.
After his brother's assassination, Abdulaziz began to assert his political position.
Championing progressive causes was a way to assert his independence — a position he exploited in jockeying for power — and to move in a glamorous international set that suited his bombastic, aspirational self-image.
