There’s a scene in the film I Heart Huckabees where Mark Whalberg’s character, (a secondary character) is about to be introduced to viewers. Two things happen in sequence to introduce him. We’re currently absorbed in a different scene with the main protagonist and his drama with two other people. A phone rings and we hear Mark W’s voice, ‘…got a serious situation happening over here…’ the scene is broken up and we cut to…
Mark standing on the lawn of his house as his fire crew buddies apologetically help his wife move out of home with his child. Mark W is berating them all with nihilistic ideas. A sub-plot is introduced, a new character is introduced and right now, it has nothing to do with the main drama in the book as experienced by the protagonist.
Introducing new characters in this way is a great way of bringing verisimilitude to your fictional world. Your protagonist isn’t operating in a vacuum, other people exist with their own feelings, issues and dramas. Next time you watch a new TV show, movie or new book, keep an awareness for how a new character enters the story and you’ll notice it happens a lot AND that it’s good!