The Galactic Republic Chancery election of 40 BBY was an election that resulted in Senator Finis Valorum of the Lytton sector succeeding Kalpana as Supreme Chancellor of the Galactic Republic. As Valorum was one of Kalpana's advisors, presumably Kalpana did not run.
Valorum was largely elected due to the recognition and influence of his family. His involvement as a negotiator in the Stark Hyperspace War was another factor that aided his election. He presumably also was helped by his accomplishments as an advisor to Kalpana.
Additionally, the Tarkin family helped elect him, in return for a promise that Ranulph Tarkin would be posthumously praised for his job in attempting to defeat the Stark Commercial Combine. The Kalpana family was also influential in securing Valorum's election.
Valorum ran under the support of the Core faction of senators.