The 1996 Star Wars spin-off, Shadows of the Empire (novel, comic book, video game, and breakfast cereal), being set between The Empire Strikes Back and Return of the Jedi, found a replacement character for Han Solo in the lovable scamp Dash Rendar. Dash not only sported Han's in-your-face attitude, he flew a nearly identical ship to the Millennium Falcon and had a wacky robot sidekick. Though hastily offed when he no longer served a purpose, Dash apparently still exists in the hazier reaches of the "Expanded Universe."
Gavin Darklighter, who is the cousin of Biggs Darklighter.
With the repeated "new Dark Lords" and "new superweapons," the WHOLE Expanded Universe should be called Shadows of the Empire!
After Ned Stark's death at the end of A Game of Thrones, Davos Seaworth shows up to serve the function of The Stoic, family and honor oriented, speaker-of-truth-to-power to a Baratheon king. They even mirror each other in interesting ways, particularly their fates (Ned is killed in a last minute whim of Joffrey's, Davos miraculously survives his ship's sinking) compared to their children's (Ned's children find ways to thrive in adversity, while four of Davos' sons are killed in battle).
Oberyn "The Red Viper" Martel was Too Cool to Live, and fans have suspected that The Scrappy Gerold "Darkstar" Dayne was created as one of these. Both men are the black sheep of their families and have badass reputations and are known by cool nicknames. More to the point, both men are from the some place and Dayne interacts with Oberyn's family members.
In-universe example: Gregor "The Mountain" Clegane, a huge, insanely strong and brutal thug is supposedly killed at the end of Book 3. In Book 5, a similar-sized knight who refuses to take off his armor called Robert Strong appears. Many characters suspect that Strong is in fact Clegane's zombified corpse.
A meta-example in Neal Stephenson's The Baroque Cycle: Daniel Waterhouse notes that some people can be replaced in their positions with only the most superficial elements changing, but other people are more crucial to the story, and their loss will forever change the status quo no matter who replaces them.
In Death series: Eternity In Death has Eve and Peabody questioning the housekeeper who worked for the murder victim. Then they go to see the murder victim's friend, whose housekeeper might have been a clone of the previous one. The story states that the two housekeepers are sisters.
Laura McCall for Taffy Sinclair in The Fabulous Five series. Even though Taffy is still present, she and the group have called a truce in the final book of the previous series and she has become somewhat nicer. Laura is the new Alpha Bitch and apparently doesn't have any of the Freudian Excuse that Taffy did (overbearing stage mother, etc.)
In The Infernal Devices: Cyril is essentially an older Thomas, brought in to replace him after his death.
In James Ellroy's novel The Big Nowhere, one of the protagonists is Buzz Meeks, a disgraced ex-Dirty Cop who has since gone on to become a crooked Private Detective, Hollywood fixer, and enforcer for Eccentric Millionaire Howard Hughes. Since Meeks was killed off early in L.A. Confidential, his role in Ellroy's Underworld USA trilogy was filled by Pete Bondurant, a character with a virtually identical backstory.
In Elmore Leonard's novel Split Images, Detroit homicide detective Bryan Hurd is an obvious stand-in for Detroit homicide detective Raymond Cruz. Cruz appeared in some of Leonard's prior work, which was being optioned at the time.
In-universe example in Vampire Academy. When Dimitri turned into a Stringoi and Rose quit her training, Lissa needed new guardians. Grant was a seasoned guardian and trainer, similar to Dimitri. Serena was a girl close to Lissa's age, similar to Rose.
The late Chicago-based author John R. Powers wrote the Last Catholic Trilogy in the 1970s, consisting of the fictionalized memoirs The Last Catholic in America (about life as a young boy going to a Catholic grammar school in the '50s), Do Black Patent Leather Shoes Really Reflect Up? (about life as a teenager going to a Catholic high school in the '60s), and The Unoriginal Sinner and the Ice Cream God (about life as a twentysomething approaching the 1970s, going to a community college, and finding a job and romance). The first two novels are narrated in First-Person Perspective by our protagonist Eddie Ryan. The third is narrated the same way by protagonist Tim Conroy, who, for all intents and purposes, is Eddie Ryan but with a different name. The reason for the switch was possibly that the third novel has a Downer Ending, where we learn that Tim dies of cancer at age 27. It may have been the case that Powers did not want to take his readers through three books, only for them to see their hero die at the end.
Dr. Carolyn McConnell, in the Eighth Doctor AdventuresDoctor Who spin-off novel Vampire Science, is a substitute for Dr. Grace Holloway, due to the novel publishers discovering late in its creation that the rights to Grace, who was created in Doctor Who:The Movie, were owned by Fox and that they weren't allowed to use her. Like Dr Grace, Dr Carolyn is a San Francisco medical doctor who had a previous adventure with the Eighth Doctor (established in the book's prologue).