Train for terrain, condition for conditions
If your running regime consists only of running on flat surfaces in decent temperatures, remember this: foot pursuits happen in all kinds of weather on all kinds of surfaces.
Consider adding variance to your workout strategy to facilitate better performance in challenging settings. Try running a diversified “cross-country” type course that requires the kinds of physical movements you might be forced to perform in a foot pursuit — things like jumping over ground obstacles, scaling a chain link fence, jumping over a wall, quickly pushing through tight squeezes between buildings or fighting your way through brush, etc.
Imagine the kinds of settings you might encounter in your area and tailor your running trail to meet the demands they may present. Also try to add weather challenges to your workout. Make an effort to run in the rain, snow, and heat depending on your local climate.
Running in a controlled-temperature atmosphere on a flat, comfortable surface is fine and necessary for a variety of reasons, but adding surface and weather variances to your workout will help you more realistically train for the kinds of challenges you could very easily encounter in the field.