The phrase 'then director of' is correct and it can be used in written English.
For example, "The company was initially led by John Doe, then director of the firm."
I was manager of stations and then director of stations.
Mrs. Lieberman was then director of the Voice of America.
Max A. Caramanian, then director of standardization and safety.
The women in the organisation, including Jenny Abramsky, then Director of Radio, were never properly involved".
Duelfer was appointed in January by George J. Tenet, who was then director of the CIA.
Frieden, then director of the CDC in the USA, had a hand in that.
From 1975 to 1986, Schmid was artistic adviser, and then director, of Opera Northern Ireland.
As defense secretary, he clashed with Mr. Bush's father, George Bush, then director of central intelligence.
Bought after lunch with Peter Hall," who was then director of the National Theater.
He introduced himself to Mark Fried, then director of writer-publisher relations.
He became the head coach, then director of player personnel and a television analyst.
