He said there had been a lot of positive change across the council and the district, particularly over the last few years.
"The last three years have been the most productive years for a long time," he said.
"There are challenges ahead, but stick to it. I want to thank my family for the interest and support they have shown me over the last three years, especially my wife Sal. I wish you all the best for the district."
Burne-Field was elected in 2016 to represent the Aramoana/Ruahine Ward.
She spoke of the successes over the last term which she was particularly proud of having "planted the seeds" for, including progress on community planning, lobbying central government for funding, safer communities and the mayor's taskforce for jobs.
She thanked the community and staff for their support and excellent work.
"We've come a long way," she said.
"We see our community thriving, and there are a lot of people involved in that, but I'm proud to have been a part of it. I believe the next council will be the best one ever."
Mayor of Central Hawke's Bay Alex Walker said it had been a privilege to work with them.
"We have had our challenges and disagreements on some issues, but we've all stood strong together as a team for the benefit of our communities," Walker said.