If more than one nomination is received, an election will be held by postal vote using the first past the post (FPP) electoral system.
A postal vote would take place from August 19 until noon on September 10.
Hawke's Bay Regional Council is made up of nine representatives elected by the community through the local body elections held every three years.
Hastings has three members, with one seat vacant due to the resignation of Graham.
Following his resignation, Graham cited his work on regional parks, Māori wards and the Napier Port IPO as his highlights during his tenure.
Rick Barker also stepped in as acting chairman after Graham's resignation.
Details on the process for candidates, enrolment, voting and results can be found on the HBRC website.