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.