Realistically, he'd probably keep his power a secret, masking it from Vader/Palpatine as well as the Jedi. He'd just use it as a tactical tool in his arsenal most of the time -- only revealing it when absolutely necessary.
Now if he ever felt that Palpatine and the Empire were a legitimate threat to the Chiss Ascendancy, Thrawn might use his powers to assassinate Palpatine during one of their meetings. Afterward, Thrawn's position as a high-ranking military official would allow him to help influence the choice of a new(and more benevolent) leader for the Empire -- a leader whose ideals closer aligned with his own. Heck, that was his ultimate goal anyway: eventually helping select the being who would replace Palpatine upon his death.
At some point after that, I assume Thrawn would return to the Chiss Ascendancy, and use his power(and newfound Imperial allies) to help combat some of the ridiculously OP threats in the Unknown Regions that he's alluded to in the past... Threats that make even the Empire look saintly by comparison.