The Big Bad needs a Number Two; this would be the Evil Counterpart of that (or The Lancer). He's the main villain's right-hand man, his closest confidant (or something akin to it), frequently acts as his Foil, and may be seen working as the front-liner of the evil forces to personally carry out his master's orders as one of his most dangerous and competent subordinates.

A Big Bad and a Dragon aren't a Big Bad Duumvirate, as this would require them to be on equal footing for it to apply. Though a Duumvirate can have one or more Dragons of their own. For literal dragons and their permutations, see Our Dragons Are Different. Not to be confused with the Dragon Lady (which describes a character stereotype, not a character's role).

Examples:

• Anime & Manga
  • Doraemon
• Comic Books
• Fan Works
• Films — Live-Action
• Literature
• Live-Action TV
• Video Games
• Web Comics
• Web Original
• Western Animation
• Other Media

Related tropes:

• Beta Bitch: Number Two to the Alpha Bitch, she often fills the Dragon role when the Alpha Bitch is the Big Bad.
• Co-Dragons: Two or more characters split the Dragon role between them.
• The Creon: A second-in-command that's happy with his position.
• Demoted to Dragon: A previous Big Bad is revealed to be, or is reduced to being, the Dragon to another villain.
• Devour the Dragon: The Big Bad kills the Dragon in order to become stronger.
• Dragon Ascendant: When he takes over from the Big Bad after the latter is defeated or leaves.
• Dragon-in-Chief: When he is more dangerous than the Big Bad and the de facto main villain of the story. Like Dragon with an Agenda, may be The Man Behind the Man. Not to be confused with The Heavy.
• Dragon Their Feet: When the Big Bad is defeated or killed first. The Dragon may or may not show up afterwards to rescue or avenge him, but he might just take his business elsewhere.
• Dragon with an Agenda: When he has different goals from the Big Bad. If those goals are mutually exclusive, The Starscream, Rule of Two or Dragon-in-Chief may be in play.
• The Heavy: The "active" villain that drives most of the plot. While this villain can be either the Dragon or the Big Bad, many authors tend to use The Dragon in order to keep the Big Bad in the background and mysterious for most of the story. Not to be confused with Dragon-in-Chief.
• It's Personal with the Dragon: When the Dragon is the hero's Arch-Enemy instead of the Big Bad.
• Lancer vs. Dragon: When the secondary hero and villain fights each other.
• Mook Lieutenant: When the Dragon is merely the leader of the Big Bad's minions when the Big Bad isn't around.
• Mouth of Sauron: When the Big Bad himself is almost never seen taking an active role, The Dragon is usually the one who picks up the slack on reminding people why they're afraid of the Big Bad in the first place.
• Noble Top Enforcer: A trope that often overlaps with the Dragon; when the Big Bad's Number Two is an Anti-Villain that is considerably more virtuous than his master. Likely to turn on the Big Bad if their actions piss him off enough.
• Number Two: The second-in-command of a team or organization, often overlapping with The Dragon.
• Number Two for Brains: When The Dragon is an idiot.
• Pre-Final Boss: A major Boss Battle that immediately precedes the Final Boss. By nature, this is often The Dragon, with the Big Bad being faced afterward.
• Rule of Two: A standard Big Bad and Dragon dynamic where betrayal is expected, and often inevitable.
• The Starscream: A traitorous Number Two; often fulfills the role of the Dragon.
• Vile Villain, Laughable Lackey: A duo consisting of a serious villain with a humorous subordinate.
• Villainous Friendship: When a Dragon is good friends with the Big Bad.