Trevor Belmont is the series' interpretation of the character of the same name who starred in Castlevania III: Dracula's Curse. Even though he does not make an actual appearance in the series, he is mentioned in the third season's episode "Return to Castlevania" (1993).
Just like in Dracula's Curse, he is mentioned to be an ancestor of Simon Belmont. In contrast to the games, however, he is his great-grandfather, while the Trevor from the Castlevania series predates Simon by two centuries. This outcome is the result from the localization changes in the American Dracula's Curse instruction booklet.
In the episode, the Poltergeist King accuses Trevor of taking credit for defeating the Count, bringing shame to Simon and his family. However, this turns out to be a plot devised by the Count himself to get him out of the way, but due to the combined efforts of Simon and the rest of the N Team, he and his son Alucard are defeated in the end.