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Mr Barclay gave in to pressure to resign after Prime Minister Bill English's involvement in the long-running saga was revealed and it threatened to damage Mr English.
It emerged this week that Mr English last year told police Mr Barclay had admitted making a secret voice recording of former electorate secretary Glenys Dickson.
Police did not lay charges, citing insufficient evidence.
Mr Barclay did not co-operate with the investigation, while publicly denying the allegations.
Yesterday, National Party general manager Greg Hamilton said the party board would consider the matter soon so the new selection could start.
Mr Barclay was re-selected last December after a bitter contest.
A group of party members who believed he needed to go backed a challenge from former funds manager Simon Flood.
Mr Hamilton confirmed the party board would consider a complaint from a group of members about the selection contest.
It is understood to involve claims of delegate stacking to skew the outcome.
He did not respond to questions about the party's wider handling of the affair.
The Otago Daily Times revealed last March that Mrs Dickson's resignation involved claims of a secret recording.
Party member Maeva Smith, a friend of Mrs Dickson, said the party needed to take some responsibility for its handling of the problem.
''We didn't want any damage to [Mr English] - that's something that we didn't want. We've got a great deal of respect for him.''
The attitude of party headquarters in Wellington was that the problem would ''die down'', she said.
''The party must carry part of the can.
''We told them six to nine months ago that you've got a problem, but no.''
Some members are blaming Mrs Dickson's supporters for damaging Mr English's career.
''It's all right, I'm a big girl; it doesn't worry me. People will say that that's Bill's one chance to be prime minister and you people have wrecked it.''
Mrs Smith said she would be working on the campaign to elect Mr English as prime minister in September.
She hoped the electorate, which has up to 1500 party members, would rebuild.
''In some ways it's cleared the air.
''We all know where we stand.
''But there will be some people very disgruntled on the other side now.
''Hopefully, we get a new candidate who has the ability to bring things together.''
Former electorate chairman Stuart Davie, who resigned last year calling his position ''untenable'', also hoped the electorate could finally move on.
It remained deeply divided, he said.
''I'm disappointed we got to this [point] but [Mr Barclay's announcement] had to happen,'' Mr Davie said.
An Otago Daily Times reporter who visited Gore yesterday to speak to people in the street said the feeling was that Mr Barclay's decision to stand down was correct.
One woman said there was a general feeling around Gore that Mr Barclay was too young for the role.
When elected in 2014, Mr Barclay was 24.
His work experience included stints in senior National MP's offices.
In his statement yesterday, Mr Barclay said he was stepping down as a candidate and would leave Parliament in September.
''I don't want the issues that are important to Clutha-Southland and all of New Zealand to be distracted by an employment dispute.
''This has been a hard decision to make, but it is in the best interests of our Government and the National Party, and I wish the Prime Minister and our team all the best for the general election.
''I got into politics because I was inspired by the people I worked for, Bill English, Gerry Brownlee and Hekia Parata. I wanted the opportunity to make my contribution too,'' Mr Barclay said.