Make Room for the New Plot

Sometimes, earlier plot elements must be quickly rushed aside in order to make room for newer ones, necessitating fast resolutions. What this usually entails is that the main thrust of the plot thus far must be resolved within a few scenes so we can hurry up and get to the new main event.

This trope can be frustrating if, until this resolution, the first plot had been portrayed as being a very difficult situation to deal with, only to be quickly solved now that the plot demands it. There are several ways around this- the main one is to turn the old problem into a sort of Worf Effect for the narrative as a whole. It establishes that, as bad as the old situation was, the new one is substantially worse, and requires our full attention without distractions. If the original part of the plot's conflict was largely diplomatic, for example, it's quite understandable that everyone is willing to put it aside to deal with the newer threat.

A relatively organic way of enacting a Halfway Plot Switch. Compare Always a Bigger Fish and Rising Conflict.

Note that this trope, nearly by definition, involves spoilers since the new plot can only really show up in the middle of the story.

Anime & Manga

 * This is how the Cell Arc starts in Dragon Ball Z. Frieza and King Cold have just gotten to Earth, ready to take revenge. Everyone is seriously alarmed by this until Future Trunks shows up and beats the crud out of both of them single-handedly. He explains that in the future he's from, there are enemies way stronger than him and the Z Warriors need to start preparing for it now if they want to stand a chance.
 * Happens near the end of Death Note, when Mello is casually defeated by Light to hasten the way to the story's grand conclusion, though Mello had been, up until that point, a very serious problem that Light had been unable to solve.

Live Action TV

 * In the first episode of Firefly, most of the conflict of the middle part of the story is about the lawman who the crew has captured, and what they're going to do with him. While some of the crew is off the ship, the lawman escapes and takes River hostage. When Mal comes back, he takes one look at the situation and shoots the lawman in the head. It's not that the consequences for just shooting the lawman have become inconsequential- but Reavers are about to attack the ship and "not being killed by Reavers" is a far more pressing immediate problem than anything caused by killing the lawman.
 * This happened in the Stargate Universe episode "Sabotage". The major plot point of the past two episodes had been several main characters who had been stranded. In the first 10 minutes of "Sabotage", they easily return to the ship, and it's not mentioned again, so that they can deal with the new plot, the sabotage.

Western Animation

 * One episode of The Simpsons has Homer trying to deal with a badger invading the back yard, but he discovers he can't contact animal control because the town's area codes have been bisected. In this case the original plot was simply ignored — Homer casually dismissed the badger when it reappears, stating that they now have bigger problems.

Other

 * A Planet for the President by Alistair Beaton has the A-plot, a B-plot of a character trying to uncover the conspiracy involved in the A-plot, and a comically odd C-plot (and a few other things). There's a very clear moment where the deadline for the A-plot looms, and so all the others are quickly cleared up to make way for the denouement.