The beginning of Star Wars: Thrawn takes place between Solo in 13 BBY and A New Dawn in 11 BBY, according to the Del Rey Books Timeline. From there, based on information given in the book, we can plot out the novel’s timeline as follows:
Between 13 BBY and 11 BBY: Thrawn is discovered by the Imperial Navy, meets with Emperor Palpatine and joins the Navy himself, starting as Lieutenant. // Arihnda Pryce signs her family’s mine over the the Empire, in an exchange for a job with Senator Renking on Coruscant.
Between 11 BBY and 9 BBY: After serving 2 years aboard the Blood Crow, Thrawn is promoted to Captain following his first encounter with Nightswan. // Pryce is fired by Senator Renking, after the incident with Moff Ghadi.
Between 10 BBY and 8 BBY: After the Umbara incident, Thrawn is promoted to Commander and given command of the Thunder Wasp. // Pryce takes a job with Higher Skies Advocacy Group.
Between 9 BBY and 7 BBY: Thrawn is promoted to Commodore and given command of the ISD Chimaera, following his resolution of the conflict between the Cyphari Afe Clan and human colonists. // Pryce is appointed Imperial Governor of Lothal after the removal of former Governor Azadi, thanks to her dealings with Grand Moff Tarkin.
Between 8 BBY and 6 BBY: Pryce officially takes office as Governor on Lothal, after serving her first year as Governor primarily on Coruscant.
Between 8 BBY and 2 BBY: Some time after his resolution of the Botajef incident, Thrawn is promoted to Admiral.
2 BBY: The Batonn Crisis. Thrawn is promoted to Grand Admiral, and transferred to Lothal Sector to assist Governor Pryce with the Rebels on Lothal.
Love how you are studying my whereabouts. Better than the Bothan Spynet.