Taking Carol Danvers
Starforce was created to support the Kree Empire in their war against the Skrulls by all means necessary. Upon learning in 1989 that Kree defector Mar-Vell has created the Light-Speed Engine to peacefully put an end to the war, the Supreme Intelligence sent over Yon-Rogg and Minn-Erva to dispose of Mar-Vell and steal the energy core. Though Yon-Rogg succeeded in killing Mar-Vell, the energy ends up being absorbed into a young pilot named Carol Danvers when she destroyed the engine. The explosion is what caused the energy to be absorbed into Carol's body, erasing her memories. Upon learning of this, Yon-Rogg took Carol as his new protege to the Kree homeworld Hala, renaming her as Vers and training her as a new member of Starforce.
Tracking Down the Skrulls
In 1995, Starforce was tasked to help track down the Skrulls (led by Talos), who have kidnapped Kree spy Soh-Larr in the planet Torfa. However, it turns out that it was all a trap to lure Vers into the Skrulls' grasp as they intend to access her memories, just as Vers manages to free herself before engaging into a fight against several Skrulls. This actions is what caused the Skrulls' ship to self-destruct, forcing Vers, Talos and a number of Skrulls to evacuate to Earth.
Upon receiving a call from Vers over her current location on Earth, Yon-Rogg leads Starforce to a 22-hour hyperjump to Earth. However, Vers soon regained her memories and learned that the Skrulls lost their homeworld to the Kree because their refusal to submit to Kree rule and that they just want to find a new homeworld to be safe from the Kree Empire. Vers also learned that before Mar-Vell died, she created a giant spaceship (powered by the Tesseract) that can be used to harbor Skrull refugees. She also remembered that she witnessed Mar-Vell being killed by Yon-Rogg before she destroyed the engine that erased her memories in the first place, realizing that she was used by the Superior Intelligence and Starforce into leading them to the Skrulls.
As Yon-Rogg finally made to Earth, he tracked down Vers' location in an old shaft, only to find out that Norex is impersonating Vers in order to allow the real Vers (along with Nick Fury, Maria Lambeau and Talos) to fly up to Mar-Vell's giant floating in Earth's orbit containing many Skrulls refuges (including Talos' wife and daughter). Realizing now that Vers has regained her memories and defected to the Skrulls, Yon-Rogg kills Norex before contacting Ronan the Accuser to send in a fleet of warships to Earth. He would later have Starforce to track down Mar-Vell's ship, where they captured Vers and the Skrulls.
The members of Starforce watch as Vers is being interrogated by the Superior Intelligence, who taunts her of her failure until Vers breaks free of the implant that was used to suppress her powers, allowing herself to free Fury, Maria and the Skrulls from captivity and have them evacuate back to Earth. Upon witnessing this, Yon-Rogg orders his members of Starforce to take Vers down, but Vers defeats them before defeating Ronan's fleet by destroying their missiles, forcing Ronan and his remaining forces to flee.
Witnessing the retreat of Ronan and his remaining forces, the remaining Starforce members are forced to retreat back to Hala (except for Minn-Erva, who was killed by Maria while attempting to take down several Skrull refugees). Even a defeated Yon-Rogg was sent back to Hala to deliver Vers' message that she would end the genocidal war for good.
It is unknown what happened to Starforce afterwards, though it can be presumed that its surviving members would face a severe punishment by the Supreme Intelligence for failing on their mission in disgrace (with the exception of Korath, who turned over to serving Ronan until his death).