Early 1800s AD
As covered in the Order of Ecclesia article, after the events of Symphony of the Night, the Belmont clan began to disappear. This forced one of the Belmonts (no one yet knows who) to pass the Vampire Killer whip off to a trusted friend for safe keeping. The whip was then passed through the line, from Master Hunter to Trainee, much like it did within the Belmont clan.
In 1820, Dracula appeared again. Although there is no game specifically tracking this event (yet), the events are detailed in the opening for Circle of the Moon. Morris Baldwin, wielder of the Vampire Killer, went to Dracula's castle and destroyed the vampire. Being only 10 years before the events of Circle, Dracula still remembers Morris quite clearly, and part of his plan is revenge on Morris for Dracula's earlier defeat.
Castlevania: Circle of the Moon
Morris Baldwin, with his two trainees, Nathan Graves and Hugh Baldwin, invaded Carmilla's castle intent on stopping the sorceress from bring the Dark Lord back to life (as all of his minions are want to do time and again). Upon reaching the ceremonial chamber, though, they find their efforts have come too late: the Dark Lord has been reborn, although he still needed time for his magic to fully build.
Dracula, confronted by three trained vampire hunters, destroys the floor beneath our heroes, plunging Nathan and Hugh down a long, vertical shaft, leaving them to hopefully die in the catacombs of the castle. Morris stands alone against the vampire, one old man to become the Dark Lord's plaything.
In the basement, Hugh and Nathan fight, with Hugh claiming the right to destroy Dracula even though Nathan was the one who gained the right to wield the vampire hunting whip (presumably the Vampire Killer, although it's called the "Hunter's Whip" in this game). After a long argument, Hugh stormed off leaving Nathan to explore the castle alone and, hopefully, find a way to the top of the castle.
Battling through the long and lengthy halls of the castle, Nathan developed his power further, gaining the use of a collection of magically enhanced cards, 10 for the elements and 10 for the gods, which when combined gave him a host of magical abilities. Using these, he fought his way to the top of the castle, only to face off with Hugh.
Hugh, enraged at the fact that Nathan had gained the Hunter's Whip, was swayed by Dracula's power, the Dark Lord controlling the trainee's rage until he had another minion under his control. The two vampire hunters fought, a battle of near equals. Nathan emerged victorious, but he didn't kill Hugh; instead, the felled hero came to his senses and swore off his need for revenge. Hugh acknowledged Nathan as the better warrior and agreed to stand aside while Nathan carried out the quest against the vampire Prince.
Fighting through the last halls of the castle, Nathan reached the central ceremonial chamber once again. There he faced off against a stronger, more dangerous Vampire Master. Hero versus villain, Nathan fought Dracula tooth and nail (or fang and claw, if you will). While the two foes battled, Hugh freed his father, Morris, and two escaped the castle. Nathan defeated the Dark Lord, and made his escape as well, the castle crumbling as the evil within was dispelled.
As mentioned above, the whip used in this game is the Hunter's Whip, not the Vampire Killer. It can be assumed that the two whips are one and the same, as the Hunter's whip never comes up again, and there is a known history, in the series, of the Vampire Killer passing from the Belmont clan to other caretakers, like the Baldwins, for a time.
The Baldwin clan is never heard from again after this game, nor is any mention made of Nathan in later games. Konami, under the guidance of series lead IGA, had removed Circle of the Moon from continuity for a time (although recently sort-of added it back in). Some speculation is that IGA was not a fan of the game and felt it was unnecessary in "his" version of continuity (although this is only speculation).
This game was the first "sequel" to the Metroidvania formula of Symphony of the Night. Much like in Symphony, our hero ventures back and forth through a large castle, collecting experience, items, and spells all to aid him in his battle against the Dark Lord. The play formula didn't diverge much between the two games, although each does have differing play-styles, partly because of the fact that Nathan is a whip-wielding hero, and partially because of the heavy emphasis of the spell system in the game (spells weren't as important in Symphony of the Night).
The spells system in the game is called the "Dual-Setup System" (DSS for short), a collection of 10 cards representing Elemental Animals, and 10 cards representing the Roman gods. The two sets could be paired up, one-to-one, for a selection of effects. Pairing Mercury (whose card applied effects to Nathan's whip) with Salamander (the animal of Fire) gave Nathan's whip a fire effect. Each of these two card combinations (one god with one animal) gave Nathan a different spell effect he could use, but only one effect could be used at a time.
This was an interesting and bold spell system although it was not without its faults. Although many of the spell combinations were interesting, few proved very useful. Additionally, the cards were hard to collect, seeming to come from a random smattering of monsters (as random kill-drops) throughout the castle, with no rhyme or reason to how you gained them or why they were carried by those monsters (as an example, the Serpent card -- Ice Serpent, so power over ice -- could be gained early in the game from an Earth Demon, since Ice and Earth are so closely related, of course).