'director executive' is a correct and usable phrase in written English.
You can use it when you want to refer to someone who has both a director and executive role within a company, such as a 'Director Executive Officer.' For example, you can say "The company hired a new Director Executive to oversee their operations."
JUAN P. OSUNA Director, Executive Office for Immigration Review, Justice Dept.
(That included a period without music director, executive director or board chairman, and a 2011 filing for bankruptcy protection, from which the orchestra emerged in late July).
In 1996 she was the director, executive producer and co-writer of a television movie called "The Christmas Tree," starring Julie Harris.
From 1967 to 1983, he worked at Bunge Corporation, an agribusiness where he held positions including Director, Executive Vice President, Treasurer, and Controller.
Dr. Pordy was still practicing medicine, but quickly rose through the corporate ranks, becoming Chock full o'Nuts's medical director, executive vice president, president and eventually chairman.
The course aims to provide students with a platform from which to work as a design director, executive, fashion direction forecaster, fashion product manager, designer-merchandiser or production service manager.
So the artistic director-executive director duo of Hytner and Starr was replaced by a new triumvirate of Norris, Ross and Burger, who been been chief operating officer under the previous regime.
Presented by the New Group, Scott Elliott, artistic director; Geoff Rich, executive director; and Tectonic Theater Project, Mr. Kaufman, artistic director, Greg Reiner, executive director.
Presented by the Transport Group, Mr. Cummings, artistic director; Lori Fineman, executive director.
Sir Elton John, Founder and Chairman David Furnish, Director Scott Campbell, Executive Director.
And Brian Ritchie, group creative director, becomes executive creative director.
