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Mr Wright, who farms at Cannington near Cave will contest the election on March 15 against Nicky Hyslop.
Mr Wright was chairman of the Central South Island Farmer Council for five years.
Mrs Hyslop owns and farms Levels Estate near Timaru with her husband Jonty. She is chairwoman of Irrigation NZ and a director and vice-chairwoman of Aoraki Development and Opuha Water Ltd.
The election will be conducted by postal and internet voting. Voting papers will be posted on February 11.
To be eligible to vote a livestock farmer must, on June 30, 2018, have owned at least 250 sheep, or 50 beef cattle or 100 dairy cattle.
The electoral roll will close at 5pm, Friday, January 25. Farmers can ring 0800 233-352 to check if they are on the electoral roll or to get a voter registration form.
-By Chris Tobin