Pirates appear only once in FreeSpace, in the Silent Threat mission Cloak and Dagger.
Alpha 1 is assigned to guard the Talus Mining Station while the GTI evacuates important warhead materials. The pirates had already attacked the station and inflicted 90% losses on the garrison, but were destroyed when a few of the warhead containers were ruptured (which created massive explosions). After several Seraphim bombers and Manticore fighters attack the station, the pirates arrive in two wings, Shi wing (two Apollo and two Anubis) and Zen (two Seth and two Horus). If the difficulty level is at least medium, Ryu (four Hercules) will arrive later. The multiplayer version of this mission is slightly different.
The pirates also snuck onboard a few Chronos freighters. They attempted to hide among the freighters heading to evacuate the weapons cargo. Alpha 1 scanned the freighters and found the ones that the pirates were using. Alpha 1 and his/her wingmen were able to destroy the pirate freighters before they escaped with the valuable weapons cargo.
See also: Pirates and Campaign Design