Continuation novel

A continuation novel is a novel in the style of an established series, produced by a new author after the original author's death.
Continuation novels may be official, produced with the permission of the late author's literary executors, or unofficial where the original author's works are now out of copyright.
Official continuations.
Where official continuations are produced, the novel will normally try to keep closely to the style of the original author in order to preserve the integrity and value of the literary franchise and the author may be legally required to do so.
Examples of official continuations include the multiple authors that have continued Ian Fleming's James Bond series, including Kingsley Amis, William Boyd, Sebastian Faulks and others; and the 2014 Hercule Poirot continuation novel "The Monogram Murders" by Sophie Hannah, produced with the permission of the Agatha Christie estate.
Some versatile authors have contributed to more than one continuation series, for instance Sebastian Faulks who in addition to James Bond has written the first ever official P.G. Wodehouse Jeeves and Wooster story, "Jeeves and the Wedding Bells", published in 2013.
If not done well, the continuation novel poses risks to the reputation of the dead author but writing one is also a risk for the new author as they are obliged to suppress their own style in favour of the style of an often better-known author and one whose fans may take convincing to accept the legitimacy of the new work. Faulks said of his Wodehouse continuation: "People said it was brave – or stupid. Either way, it was a ridiculous undertaking. PG Wodehouse is, by common consent, one of the great prose stylists of the 20th century. I didn’t want to make a mess of it."
If the continuation is a success however, it may lead to substantial sales and, just as importantly, revive interest in and sales of the works of the dead author. For this reason publishers will sometimes commission a continuation novel if they feel that interest in the original author is beginning to wane.
Unofficial continuations.
Where the original works are out of copyright, however, the new author(s) are free to interpret the franchise in any way they wish. There are a large number of Sherlock Holmes continuations for instance which vary in quality and authenticity. Such unofficial continuations, which may overlap with fan fiction and pastiche, may introduce completely new characters, change time periods, add or remove plot elements and make as many changes to the original formula as the author feels are useful.