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Dr Slee declined to comment on the reason for her resignation last week.
It is the second time in six months the board, which is responsible for an area from Duntroon to Lake Ohau, finds itself one shy of the five required members.
Only four people put their names forward for election to the board last November. Peter Ellis was subsequently elected unopposed in a December by-election.
Dr Slee brought considerable experience to the role she began last year.
She had previously served as Waitaki's Environment Canterbury councillor from 2004 to 2007, and was the Waitaki District Council’s Ahuriri ward representative from 2013 to 2016.
Board chairwoman Vicky Munro said she was grateful for Dr Slee’s contribution.
Waitaki Mayor Gary Kircher said it was a pity to lose her from the board.
"She has been a very strong candidate for the Ahuriri ward and for the Waitaki district in her different roles.
"She put her heart and soul into the different positions she has held over the years."
Waitaki District Council Ahuriri ward councillor Ross McRobie said Dr Slee was a very "diligent and thorough person".
"She is very detailed in her research and in her understanding of issues."
The Waitaki District Council is seeking nominations to fill the vacancy, which open on Monday and close on July 6 at noon.
If an election was required to fill this vacancy, it would be held on September 1 and conducted by postal voting under the first-past-the-post electoral system.