"filling the position" is a correct and usable phrase in written English.
You can use this phrase when you are talking about someone who has been chosen to replace someone else in a job or role. For example, "John has been chosen as the new manager, filling the position left open by Susan's resignation."
In 1968 Mr. Lourie moved to New York, filling the position of manager of contemporary artist relations at Columbia Records.
The Boston Beer Company, the maker of Samuel Adams beer, has hired William Urich as chief financial officer, filling the position after a five-month search.
When he was cast as Bond, filling the position most recently vacated by Pierce Brosnan, Mr. Craig did not seem like an obvious choice.
JPMorgan Chase & Company has named Tom Lee chief United States equity strategist, filling the position formerly held by Abhijit Chakrabortti who has joined Morgan Stanley.
There just seems to come a game when the players charged with filling the position assume the responsibility to do more than just react.
The Braves saw him as a future catcher, and their trouble filling the position led them to rush Williams into action at the major league level.
More than sevn months have passed since Richard E. Oldenburg, the museum's director, announced that he planned to step down this June, and the museum board, to its surprise and consternation, has been having a rather hard time filling the position--such a hard time, in fact, that Mr. Oldenburg has reportedly offered to stay a while longer.
Orange and Fairfield, for example, looked for new superintendents for about a year before filling the positions.
"I don't think they're going to have a hard time filling the positions.
The government, now recruiting passenger screeners at almost every commercial airport, is having a hard time filling the positions.
"It will be not filling the positions".
