Ha jogi szöveget fordítasz, ezt a megoldást javaslom. Köznyelvi alakja lehet chase a hot lead vagy hot trail is, de az idézett szöveg hivatalos rendőrségi jegyzőkönyvre enged következtetni.

Hot Pursuit (legal definition)

A doctrine that provides that the police may enter the premises where they suspect a crime has been committed without a warrant when delay would endanger their lives or the lives of others and lead to the escape of the alleged perpetrator; also sometimes called fresh pursuit.

Countless crime dramas have portrayed police officers in a high-speed chase barking into their radio that they are "in hot pursuit" of a suspect. This popular image says little about the legal rule of hot pursuit.
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Hot pursuit is one such exigent circumstance. It usually applies when the police are pursuing a suspected felon into private premises or have probable cause to believe that a crime has been committed on private premises. The Supreme Court stated that "'hot pursuit' means some sort of a chase, but it need not be an extended hue and cry 'in and about the public streets'" (United States v. Santana, 427 U.S. 38, 96 S. Ct. 2406, 49 L. Ed. 2d 300 [1976]). Hot pursuit also applies when the lives of police officers or others are in danger. Thus, the Court has recognized two specific conditions that justify warrantless searches under the rule of hot pursuit: the need to circumvent the destruction of evidence, and the need to prevent the loss of life or serious injury.
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The other two police cars in hot pursuit bound down onto the fairway...

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Note added at 5 hrs (2014-08-02 14:58:55 GMT)
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Az idézetben szerepel: forrónyomon üldözésre, letartóztatásra tett intézkedések - (law enforcement) actions such as hot pursuit and arrest
két példa:
http://www.fdle.state.fl.us/Content/getdoc/49f6f7d9-d436-43a...
The "Hot Pursuit" exception to the warrant requirement permitted officers to pursue the defendant through the open door of his home to effect an arrest inside, even though the crimes witnessed by the officers were only misdemeanors.
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és tengereken is ezt használjuk:
http://www.law.washington.edu/Directory/docs/Allen/Publicati...