Manhunt
A manhunt was an extensive search for a fugitive.

After the bombing of the Kelvin Memorial Archive in an alternate reality 2259, admiral  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. ()

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. ()

After Kovin turned hostile, a  crew investigation of him turned into a manhunt. ()

Legal procedures