An author was a writer of a play (TV: The Shakespeare Code) or book. (TV: The Unicorn and the Wasp)
William Shakespeare was an author of plays. In 1599, Martha Jones repeatedly chanted "Author!" following a performance of Love's Labour's Lost before asking the Tenth Doctor if that was what people did. When the crowd began chanting as well, the Doctor observed "they do now". (TV: The Shakespeare Code)
The works of Agatha Christie were in print billions of years after her death, establishing her as the best-selling author of all time. (TV: The Unicorn and the Wasp)
In an alternate reality, Panda was an author. He wrote a hugely successful novel, but Iris Wildthyme snuck in a secret message which would eventually destroy Panda's career, driving him to suicide. (PROSE: Framed)