Labour is advertising for a new general secretary to replace Peter Watt, who quit over the proxy donations scandal.
Mr Watt quit after less than two years in the post
The advert in The Guardian promises "an exciting and challenging executive position" and seeks someone able to "drive through... cultural change".
Duties include leading the party's staff and ensuring "we are compliant with all relevant legislation".
Mr Watt stepped down in November after admitting he knew businessman David Abrahams was donating cash via proxies.
The 37-year-old former nurse told Labour's ruling National Executive committee he was not aware he had broken the rules.
Scotland Yard is now investigating the matter, at the request of the Electoral Commission.
In his resignation statement, Mr Watt said he had always "prided myself on having complete integrity" but added that, as general secretary, he was legally responsible for the reporting obligations for the party.
He added: "I was aware of arrangements whereby David Abrahams gave gifts to business associates and a solicitor who were permissible donors and who in turn passed them on to the Labour Party and I believed at the time my reporting obligations had been appropriately complied with."
Under the law, those making donations on behalf of others must give details of who is providing the money.
Prime minister and Labour leader Gordon Brown has also asked party veteran Lord Whitty to hold an internal inquiry.
In a quarter page advert, in The Guardian's Society jobs section, the Labour Party says the new General Secretary will "be able to drive through organisational and cultural change in conjunction with Leadership of the party".
It goes on: "The General Secretary of the Labour Party is the person who leads the staff of the party; who prepares the party for elections, who manages relationships among and between all party stakeholders, who ensures that sufficient resources are in place, who ensures that we are compliant with all relevant legislation and who upholds the constitution of the party and the values the party represents."
Among other qualities, applicants must have a "track record in cultural change" and "financial and resource management experience at the highest level".
The party promises a "competitive salary including a final salary pension scheme".
Potential applicants are asked to call for a "confidential discussion" with Labour Party officials.
Mr Watt had been Labour's General Secretary since 2005.
His predecessor, Matt Carter, also left after less than two years in the post. He was subsequently questioned by police over his alleged involvement in the cash-for-peerages affair.
The investigation was wound up on July last year, with no charges being brought.
In the past, the job of general secretary has gone to candidates with a strong Labour Party or trade union background.
A Labour spokesman declined to comment on whether the party was seeking to cast the net wider this time.
"The advertisement will speak for itself," he said.
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