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Being the leader of the Kree Empire and ruler of its homeworld Hala, the Supreme Intelligence can choose to speak with any of its subjects by manifesting itself in the form of what the person desired. When Starforce member Vers arrives to meet the Supreme Intelligence, the latter takes the form of the late Wendy Lawson/Mar-Vell (a close friend of Starforce team leader Yon-Rogg). Being aware of Starforce's next mission of dealing with a group of Skrulls (led by Talos), the Supreme Intelligence tells Vers to take control of her emotions in check and that the Skrulls must be stopped at all costs.
Showing Its True Colors
Though Vers was able to track down Talos and several Skrulls taking refuge in Earth after being briefly kidnapped by them, she learns of a horrible truth: Mar-Vell defected to the Skrulls after learning that they just want to find a new homeworld to be safe from the Kree Empire after their original homeworld was destroyed on the orders of the Supreme Intelligence because of their refusal to submit to Kree rule. Vers also learned that she was once a human pilot named Carol Danvers who witnessed Mar-Vell being killed by Yon-Rogg when she tried to destroy the energy source that he and Starforce was after, and that she absorbed the energy after destroying the engine that briefly erased her memories.
She is also horrified to find out that the Supreme Intelligence briefly altered Vers' memories to make it look like the Skrulls murdered Mar-Vell in order to gain her trust. Because of this horrible revelation, Vers realized now that she was tricked by the Supreme Intelligence to lead the Skrulls for itself to wipe out from the universe. Infuriated of being used by the Supreme Intelligence, Vers furiously defected to the Skrulls and helped out in tracking down Mar-Vell's ship containing Skrull refugees, but they are tracked down by Starforce, who managed to track down the ship after killing Talos' right-hand man Norex. Vers is then interrogated by the Supreme Intelligence for her betrayal while the Skrulls are held prisoner by Starforce.
During Vers' interrogation, the Supreme Intelligence taunts Vers before reminding her that the energy that she's utilizing could be taken away, which would leave her powerless. However, being unwilling to submit herself further into its control, Vers frees herself from the implant that suppresses her powers and vaporizes the Supreme Intelligence's avatar. Vers then allows the Skrull refugees to escape back to Earth while defeating Starforce and foiling Ronan's fleet attack on Earth.
Following the retreat of Ronan and his remaining forces, Vers tasks a defeated Yon-Rogg with delivering a message to the Supreme Intelligence, proclaiming that she would return to put an end to the genocidal war.
It is uncertain of what became of the Supreme Intelligence following Yon-Rogg and Starforce's retreat back into Hala, though it's likely that it severely punished them for their failure after Yon-Rogg delivered Captain Marvel's message. It's suggested that the Supreme Intelligence was destroyed by Captain Marvel at some point in time, while it could also be inferred that the Supreme Intelligence is still existing, but now lacks supreme power. The former appears to be more likely, given the mentioning of a Kree Emperor who has taken over the Empire before signing a peace treaty for the Kree and Xandarians in Guardians of the Galaxy.
The Supreme Intelligence is mostly mysterious, able to take on many forms to many of its subjects. When evaluating Vers, the Supreme Intelligence presented itself as wise, careful, and understanding. This was seen in the way that Supreme Intelligence advised Vers to focus less on the mystery of her past and more on her current duty to fight for the good of the Kree Empire. To make someone a member of the Kree Empire, the mysterious ruler was not above tricking and lying to the person. This was demonstrated when it assured Vers that the Skrulls were responsible for having removed her house, her family and her memory. However, its true facade eventually shows up as it proved to be insensitive, arrogant and completely despising the humanity of Danvers, judging that it was her greatest weakness.
The Supreme Intelligence taking the form of anyone familiar to its recipient.
The Supreme Intelligence assuming the form of Mar-Vell to Danvers.
The Supreme Intelligence showing its true colors after Danvers remembers her past.
The Supreme Intelligence mocking Danvers as it overpowers her.
The Supreme Intelligence firing at Danvers after the latter began unlocking her true power.
The Supreme Intelligence realizing that Danvers is escaping.
There was a deleted scene in which Yon-Rogg paid a visit to the Supreme Intelligence, who adopted Yon-Rogg's appearance before reprimanding Yon-Rogg for killing Mar-Vell and letting Carol absorb the power of the Light-Speed Engine. The Supreme Intelligence later orders Yon-Rogg to track down Carol and bring her back so that they could disable their powers and get the Tesseract.
The Supreme Intelligence's trait of appearing different to everyone who views it is similar to how Galactus is portrayed in the comics.
If the Supreme Intelligence is still existing by the time of the current movies, it's likely that it survived Thanos' death wave at the end of Avengers: Infinity War because as an artificial intelligence, it isn't technically a living nor sentient being.