Only one alien ever entered Palpatine's inner circle in Star Wars: Grand Admiral Thrawn. Palpatine deliberately established his Empire in the Galactic Core, the sector of space where humans were greatest in number - indeed, where they were believed to have evolved in the first place. He created a power system that left humans in charge and aliens crushed underfoot, although it's difficult to say where the Emperor himself shared this xenophobia. He may well have inherited a dislike of non-humanoids from his homeworld of Naboo, where there was notable division between the Naboo and the Gungans.
Only one alien ever rose through the ranks of the Empire, attaining the position of Grand Admiral. As shown in the comic miniseries Star Wars: Thrawn, written by Jody Houser with art by Luke Ross, adapted from the novel by Timothy Zahn, Thrawn was a Chiss exile, discovered by an Imperial expedition into Wild Space. The alien had crossed paths with Anakin Skywalker once before during the Clone Wars and attempted to use that connection to impress the Emperor - the man he swiftly recognized as the former Chancellor he had been told of years before, Palpatine. But Anakin's influence was not the real reason the Emperor trusted Grand Admiral Thrawn.
Palpatine sought knowledge of the Unknown Regions. According to Chuck Wendig's Aftermath trilogy, the Emperor sensed something deep in the Unknown Regions - a vergence in the Force unlike any other, offering power he longed to claim. It is likely this was the Sith planet Exegol, a place where the veil between life and death was unusually thin, ultimately the key to Palpatine's quest to conquer death. There is no evidence Thrawn knew of the location of Exegol; it was hidden in what the Chiss referred to as a "box system," one where hyperspace anomalies meant there was only one way in or out. Still, Thrawn's information surely proved useful in helping the Emperor locate this ancient Sith redoubt. He claimed it as his own, establishing a force there that would evolve into a Sith cult dedicated to Palpatine's worship.
Thrawn Proved To Be A Useful Ally Of The Empire
Grand Admiral Thrawn became one of the Empire's top operatives. He was a military and strategic genius, which he displays this in the very opening of Star Wars: Thrawn, where he is seen taking out entire squads of stormtroopers on his own before sneaking onto an Imperial ship. As a Grand Admiral, he excelled at getting inside his enemies' minds, and thus deducing their tactics. This frequently allowed Thrawn to achieve seemingly miraculous victories, striking at a precisely-deduced blind spot to take down his foes. He would deliberately leave openings for his opponents to take advantage of, only to reveal it was a trap. Palpatine threw Thrawn at some of his greatest threats - but he lost the Grand Admiral in Star Wars Rebels season 4. Jedi Padawan Ezra Bridger managed to launch Thrawn's flagship into hyperspace, and he was lost.
As useful as Thrawn may have been, though, he actually had an agenda of his own. Thrawn had never truly been exiled at all; it was all a trick, a fiction orchestrated to infiltrate the Empire. As told in Timothy Zahn's novels, Thrawn ferried intelligence and even key allies into Chiss space, strengthening his race against both the myriad threats of the Unknown Regions and the potential hazard posed by the Empire. Palpatine may have trusted Grand Admiral Thrawn as one of his top agents, but this particular Star Wars villain took advantage of that trust.