The chancellor, Philip Hammond, has kicked off the process to find a new governor of the Bank of England, appointing a head-hunting firm that specialises in diversity and placing women in top roles to conduct the search.

The recruitment process has begun nine months before Mark Carney’s departure date on 31 January 2020 and is being carried out by Sapphire Partners, a London recruitment firm founded by a former investment banker and run by an all-female management team. The deadline for applications is 5 June.

Carney, who took up the role of governor on 1 July 2013 when he was appointed by the then chancellor George Osborne, has twice extended his tenure in response to the Brexit vote. He was originally due to leave in 2018.

Hammond said Carney’s “steady hand has helped steer the UK economy through a challenging period” and the Treasury was looking for someone with equally high-level international connections to succeed him.

Speaking to MPs on the Treasury select committee, the chancellor said: “As we leave the European Union it’s very important that the UK continues to play an important role in global fora. The governor of the Bank of England plays a very significant role in the international discussions between central bank governors and I think it’s very much in our interests that we have somebody who is recognised and respected at the highest levels of the international central bank circuit.

“We know from the experience of the previous crisis that it is through cooperation between central banks that we ensure stability. Therefore, it’s very important that as well as having someone who can do a first-class job at home, we have someone who commands respect in the international arena.”

Search begins for next Bank of England governor - business live Read more

Carney was praised for responding with authority and calm in the immediate aftermath of the EU referendum. However, the Bank’s predictions of a short-term shock to the economic growth failed to materialise. During his run as governor, UK interest rates have only changed three times and remain at only 0.75%.

Previously the head of Canada’s central bank, Carney was paid £881,574 in the year to the end of February. The package included basic pay of £480,000, an annual £250,000 allowance “to reflect the additional cost of living in London rather than in Ottawa” and £147,000 towards his pension.

Internal candidates for the job potentially include Ben Broadbent, the Bank’s deputy governor for monetary policy, and Andrew Bailey, the chief executive of the Financial Conduct Authority. Bailey is the bookmakers’ favourite, with Coral making him 2/1 favourite.

Others considered to be in the running include Raghuram Rajan, the University of Chicago professor whose previous roles include head of the Reserve Bank of India and chief economist of the International Monetary Fund.

The Bank of England has never had a female governor and the Treasury will be under pressure to prove it has taken all possible steps to find candidates.

Last year, the chancellor faced criticism when the only man from a shortlist of five candidates was appointed by the Treasury as the latest member of the Bank’s Monetary Policy Committee, which sets interest rates. Jonathan Haskel was selected to join the nine-strong MPC, which includes only one woman – Silvana Tenreyro.

Shriti Vadera, the chair of Santander UK; Janet Yellen, the former head of the US Federal Reserve; Sharon White, the chief executive of Ofcom; and Dame Minouche Shafik, director of the London School of Economics, are all potential contenders for the governor role.

Sign up to the daily Business Today email or follow Guardian Business on Twitter at @BusinessDesk

Sapphire Partners has worked for the Treasury to fill high-profile roles before. Earlier this year the firm placed Dame Colette Bowe and Dame Jayne-Anne Gadhia have been appointed as external members of the Bank’s financial policy committee. Bowe is chairman of the Banking Standards Board and Gadhia was chief executive of Virgin Money.

In an interview with the Guardian last year, the firm’s managing director, Kate Grussing, criticised companies for “putting token women on their boards” and described the excuses given by many firms for not appointing more senior women as “truly disgraceful, lame and lazy”. On its website, Sapphire says that 60% of the executives it has placed over the past four years have been women.

Interviews for the Bank job will be held in London over the summer and the successful candidate will be named in October.

Hammond said he hoped the successful candidate would commit to a full eight-year term but he would be willing to consider an alternative arrangement for an exceptional candidate.