Multiple realities
(covers information from several alternate timelines)
For the TNG episode of the same name, please see "Manhunt".

A manhunt was an extensive search for a fugitive.

After the bombing of the Kelvin Memorial Archive in an alternate reality 2259, admiral Alexander Marcus ordered the senior command of all vessels in the region to begin a manhunt for John Harrison. However, this plan was cut short by Harrison's attack on the Daystrom Conference Room. (Star Trek Into Darkness)

Any time an unusual crime was committed on Deep Space 9, Quark ran a "manhunt pool" to bet on how long it would take for Odo to catch the perpetrator. It was very popular. (DS9: "Crossfire")

This pool was the subject of the Strange New Worlds 2016 short story "The Manhunt Pool (β)".

After Kovin turned hostile, a USS Voyager crew investigation of him turned into a manhunt. (VOY: "Retrospect")

While not explicitly termed as such, the hunts for Roga Danar and for the Krajensky imposter were also a clear example of manhunts.
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