Mystery Writer Detective

Simply put, a mystery writer who solves actual crimes. After all, who better to unravel all the twists and turns of a mystery than someone who creates them for a living? Possibly a result of Write What You Know.

Compare Most Writers Are Writers, Interdisciplinary Sleuth. See also Mystery Fiction and Detective Fiction.

Anime & Manga

 * The leads from Kamen Tantei kind of subvert this. Yes, they're mystery writers who investigate mysteries. But the female lead, especially, is a "fairplay" mystery writer living in a world where ghosts, psychic powers, "all a dream" endings and fictional characters come to life (including the title character) make it impossible to use logic and common sense to actually solve mysteries.
 * Detective Conan: The protagonist's father is a mystery writer who occasionally steps in to solve mysteries when his son is stumped.

Comic Books

 * Gabe Webb from The Maze Agency
 * Kaye Daye, one of the Mystery Analysts of Gotham City.

Literature

 * Ellery Queen
 * Author Avatar Ariadne Oliver from various Agatha Christie novels
 * Harriet Vane from the Lord Peter Wimsey novels is another example.

Live-Action TV

 * Jessica Fletcher from Murder She Wrote
 * Castle
 * The Snoop Sisters
 * Temperance Brennan, from Bones. She writes mystery novels, and she also helps solve crime. Although her career as a forensic anthropologist is probably more important to her ability to solve crimes than her alleged skill as a writer.

Real Life

 * A Real Life partial example might be Sir Arthur Conan Doyle. From The Other Wiki: "Conan Doyle was also a fervent advocate of justice and personally investigated two closed cases, which led to two men being exonerated of the crimes of which they were accused." See here.
 * Granted, Conan Doyle had actual forensic training, and he had been a detective and lecturer himself before writing the Sherlock Holmes stories.