2061: Odyssey Three opens with the reveal that Dr Chandra died while in hibernation on the journey back to Earth after the events of 2010: Odyssey Two, and furthermore that everyone aboard the Leonov died over the following 46 years except for Floyd and Zenia.
William Smithback Jr. survives numerous life-threatening elements in six different books. Then Cemetery Dance comes in and he gets stabbed through the heart in less than ten pages.
Assassin (Alex Hawke Series #2) by Ted Bell - Victoria Sweet, the love interest from Book 1, more or less literally bites the bullet by the end of Chapter 1 Book 2.
In the first book of the Arabus Family Saga young adult book series, War Comes to Willy Freeman, the eponymous character's Uncle Jack plays a role in the story. In the opening paragraphs of the sequel, Jump Ship To Freedom, that story's narrator, Jack's son Daniel, informs readers that his father has recently died.
The Cat in the Stacks Mysteries: Peter Vanderkeller, Athena College's library director (and Charlie's boss) in the first six books, abruptly sent in a resignation letter in book 7; he is later discovered to have been murdered, and the letter was sent by his killers to delay the discovery of their crime.
Empress Nerissa and her entire family die offscreen in a bloody assassination just before the opening scenes of the second book of Patricia Bray's Chronicles of Josan trilogy. Considering her importance in the first book, this comes as a bit of an immediate shock, but it isn't done wastefully or for no reason. Her death shapes the circumstances surrounding Josan's life for the entire rest of the trilogy.
C.S. Lewis kills off Tumnus, Mr. and Mrs. Beaver, and all the other supporting characters from The Lion, the Witch, and the Wardrobe by setting the sequel Prince Caspianhundreds of years into the future in Narnian time.
Then in The Last Battle, Eustace and Jill learn that their friend from the last book, Rilian, "has been dead for over two hundred years." Presumably Puddleglum has, too. In fact, that book begins with the deaths of everyone from our world who ever visited Narnia, exceptSusan, in a train crash. But due to Narnia doubling as some kind of entrance to the afterlife, nobody actually notices they're dead until the end.
Early in the Discworld novel Soul Music, the second book in the Death subseries, we're told that Mort and Ysabell died in a coach crash following the events of Mort.
In the Dragons of Requiem prequel trilogy Dawn of Dragons, Prince Sena Seran is set up to be a main character in Requiem's Song. Two chapters into the sequel, Requiem's Hope, he hangs himself.
In the third book of The Elric Saga by Michael Moorcock, Count Smiorgan Baldhead, who had traveled with Elric in the last book, gets unceremoniously abandoned by Elric and left to his death during the battle with Melnibone. However, Elric does get called out on it. It also turns out that this is actually an inversion, since Smiorgan's death occurred in the very first Elric story ever published. However, that story was relatively far into Elric's continuity, so he got brought back later for another story set earlier. Later collections published the stories in their order in continuity, rather than the order they were originally published.
A hallmark of the Erast Fandorin novel series. If a character from a previous Fandorin book pops up in a new one, there's a pretty good chance that character is gonna die.
The first is Count Zurov, a pivotal character in Fandorin #1, The Winter Queen (at one point he saves Fandorin from being murdered by the bad guys). Zurov pops up again in Fandorin #2, The Turkish Gambit, only to be murdered by the bad guy as part of the bad guy's espionage plot against Russia.
A lot of characters in the Gone series. Chunk, the Coates Academy toadie gets killed (albeit unintentionally) by Caine when he gets thrown into a wall in Hunger.
The Hardy Boys: Iola Morton, Joe's girlfriend, a regular character from the original series, gets blown up in the very first chapter of the Casefiles series.
In Harry Potter with one major character dying in the climax of every book since Harry Potter and the Goblet of Fire, Rowling had settled major character death into a predictable, albeit terrifying pattern. Cue Harry Potter and the Deathly Hallows, and Harry's faithful owl Hedwig dies. In chapter four. Soon followed by the off-screen death of Mad-Eye Moody. For those who thought losing Hedwig and Mad-Eye was bad enough, the fans certainly did not expect 10+ more major characters to die. J.K. Rowling was trying to set a dismal, almost dystopian tone for her seventh and final book; she said after book five that, since it was a war, characters would get killed, even major ones.
In the first chapter of Eldest (Book 2 of the Inheritance Cycle), Ajihad is killed by Urgals, and Murtagh is presumed dead as well (although he isn't really). Also, the Razac are killed early in Brisingr.
In Island of the Blue Dolphins, the protagonist, Karana, survives alone on an island for eighteen years, and is rescued at the very end. In the sequel, Zia, Karana dies within a few months of the rescue. Justified because Karana is based on the Lone Woman of San Nicolas Island, who similarly died less than two months after her arrival at the Santa Barbara Mission.
The Jekyll Legacy (by Robert Bloch and Andre Norton): The original novel ended with Poole and Utterson discovering Hyde's body, and then reading the three messages Jekyll left behind. Early in this sequel, set just a few months later, Poole is abruptly murdered in the same manner as Sir Danvers Carew (bludgeoned to death), while Utterson subsequently dies in the same manner. It turns out to be the doings of a woman who'd unwittingly consumed the Hyde formula some months before Jekyll and Hyde's deaths, without either identity ever being aware of her doing so, and embraced her dual nature; she's now seeking to claim Jekyll's estate for herself and to kill anyone who knew Jekyll's secret, including the doctor's recently-arrived niece.
In the first book, the character Genarro actually lives, and isn't ignominiously eaten while on the toilet like he was in the movie. He even gets to beat up a raptor. By the second book, he's died of dysentery.
Accidental inversion in that Ian Malcolm, the main character of the second book, dies at the end of the first one. He gets better, though.
An interesting case happens in the Stephen King novels Desperation and The Regulators, which are not actually sequels to each other but twinners (2 books that feature the same characters, but are set in separate fictional universes). In Desperation, Mary Jackson and David Carver are two of the only four people who make it all the way to the end of the story. In The Regulators however, they are among the first three (four if you include Hannibal the dog) victims to fall to Tak's creations before the end of the fourth chapter.
The Lord of the Rings: Boromir survives all through The Fellowship Of The Ring only to die in the very first chapter of The Two Towers after an off-screen skirmish (that arguably started at the end of the first book). Subverted in the movie adaptations, where he is killed at the end of the first movie, possibly to hype up The Climax.
The main character of Raymond E Feist's Mistress of the Empire series spends the first two books in various political machinations to secure her title and lands. The triumph of her goal is to have a son, who dies in a faked accident two pages into the third book.
Uncle Press, the uncle of Bobby Pendragon, is killed off in the second book of the The Pendragon Adventure series, so that Bobby can take his role as head Traveler in the fight against Saint Dane.
Precious dies in the first chapter of the sequel to Push, The Kid, when her son Abdul is 9. Justified Trope because Precious was diagnosed with HIV shortly after he was born.
Between books 11 and 12 of Ranger's Apprentice, Alyss and Crowley have both died, and King Duncan is on his deathbed. Also, Halt is retired.
In Redwall, Friar Hugo survives the entire first book, even being held hostage by one of the entire series’ most dangerous villains in the climactic battle. In the third book (chronologically, the next after the first one), he is killed off-screen in one of the first chapters.
Shadow Moon, the first of the Chronicles Of The Shadow War sequels to the movie Willow, kills off Madmartigan and Sorsha in the first chapter.
Shattered Realms, the Sequel Series to The Seven Realms Series, kicks off with the assassination of Han Alister in the first couple chapters of the first book. This, unsurprisingly, has a major impact on the events that follow.
Stephen King is unsurprisingly fond of these; they happen not only in his direct sequels, but can crop up almost anywhere thanks to his extensive Canon Welding:
They survive the events of The Shining, but by the time Daniel Torrance has to deal with a new threat in Doctor Sleep, both Wendy Torrance and Dick Hallorann are long dead (only to be expected in Dick's case and not entirely shocking even in Wendy's, since it's more than 30 years later).
In Cujo Sheriff George Bannerman, a recurring character in Stephen King's early Castle Rock stories, shows up briefly towards the end to be brutally ripped apart by the titular dog.
Despite the whole plot of The Talisman being about saving Lily's life, Black House reveals that her cancer eventually returned and she died; but the two books are separated by a twenty-year Time Skip and her death is hinted to have taken place not too long before the start of the sequel, so Jack didn't have to grow up without his mother, at least.
Needful Things mentions that the protagonist of The Dark Half, despite surviving the events of his novel, nevertheless eventually committed suicide due to the traumas he endured.
When he reappears in Wolves of the Calla, Father Callahan reveals that the adult protagonist of 'Salem's Lot eventually died, although not until his adopted son had reached adulthood, meaning he had at least a decade or so of by all accounts good years after the end of the novel. (It's worth noting, however, that he describes Ben as living to be elderly but Mark only being in his early twenties when he delivered his father's eulogy, despite there being only a 20-ish year age difference at play; it could be that what Ben went through prematurely aged him, but it's equally likely just a case of Writers Cannot Do Math.)
Return of the Wolf Man: One of the survivors of Abbott and Costello Meet Frankenstein is killed off in the novel's prologue, which also reveals that one of the characters from House of Dracula was killed by Talbot shortly after the events of that film.
