Th kind of plot looked at today involves a chase. Good guy versus bad guy. We see this a lot in many action adventure stories. The hero/heroine may be chasing the villain or the opposite could occur. There are a number of points to remember when deciding to use a pursuit or chase plot.
The chase is more important than the people involved in the chase. Characters in this kind of story may have personalities and be interesting but the chase is the most important part of the story. Think Sherlock Holmes.
There must be a real threat that the character being chased may be caught. No danger, no fun. Many times elements of the chase plot find their way for a segment in other types of stories.
The person doing the chasing be he or she be villain or hero/heroine must have a good chance of catching their quarry. If not the reader will wonder what's the point of the story. A lot of almost captures brings an element of danger and excitement into the story.
The story and the characters should be unique, engaging and stimulating. Think of a roller coaster ride with twists and turns heading to the top and then the dive down. Scenes like this will be needed.
Try to make your characters and situations not the standard stock characters. Give the people unique quirks and the places they are chased through.
Aim for a small area. The smaller the area of the chase the more tension will grow. A single building, a small town, an island.
When writing this kind of story during your planning make sure you set the ground rules for the chase, establish the stakes and have a motivating incident. For example the spy is stealing a secret in a large office building, the hero comes into the action. The fate of the world is in his hands. The hero will win or the spy will escape. The choice is yours. Just remember to keep the scenes moving rapidly with those roller coaster highs, the swoops down and the build up to the next high.
Whether you use this as the main plot or use elements of this in another plot remember to keep the characters moving and the near hits and misses plausible.