Remember the New Guy?/Playing With

Basic Trope: A new character appears with the implication that they've always been there, just off-screen.

Straight: Bob's brother Charlie becomes a regular character in the show, despite the fact that Bob has never previously mentioned him.
Exaggerated: Charlie becomes the main character on the show, and it is suggested that he had a heavy influence on the events of previous episodes, despite not being seen or even mentioned during that time.
Justified: Bob had good reasons for not mentioning him e.g. he thought that his brother had died in a car accident, and didn't talk about it because it upset him so much.
Inverted: Charlie, previously a regular character in the show, suddenly disappears, but everyone constantly mentions him as though he was still there.
Subverted: It seems like Charlie popped up out of nowhere, but it turns out that he was actually subtly alluded to in previous episodes, and so his appearance isn't so out of place after all.
Double Subverted: Then it turns out that the characters were actually referring to someone else entirely in those situations.
Parodied: Charlie literally appears out of thin air, and Bob casually sparks a conversation with him, to the bewilderment of everyone else.
Deconstructed: Charlie ends up becoming The Scrappy, which can even lead to fans refusing to watch the show anymore.
Reconstructed: Charlie gets some Character Development, and the fans decide that his inclusion in the show, if abrupt, wasn't so bad after all.
Zig Zagged: Charlie is in episode #5, disappears for several episodes at a time and no one remembers him, then reappears in episode #11.
Averted: Either Charlie was there from the start, or when he's introduced it's made clear that he's new to the show.
Lampshaded: "Hey Alice, you remember my brother Charlie?" "Actually, no I don't, seeing as how you've never mentioned him before"
Invoked: Characters show up for the sole purpose of gags.