A chief constable has announced that he is stepping down after being asked to re-apply for his own job by the newly elected independent police and crime commissioner.

Colin Port, who had been chief constable of Avon and Somerset police, said he had "no intention" of applying for the job he has done for the last eight years.

Port met with the new police commissioner (PCC), Sue Mountstevens, on Wednesday, the day she took her oath of impartiality following Friday's election results. His contract expired at the end of January and could have been extended year on year.

But Mountstevens told Port that she wanted to advertise his job so that she could appoint a chief for her whole three and a half year term of office. The new PCC, who had worked with Port over the last two years when she sat on the now-disbanded police authority, told him he could apply for the post.

In a statement issued on Thursday, Port said: "She told me she intends to start the process to recruit a chief constable to take Avon and Somerset forward. I told her I had no intention of applying for my job.

"I can confirm that I will be retiring from the police service on 26 January 2013 at the end of my fixed-term appointment. In effect, I will be leaving considerably sooner.

"I am terrifically proud to have led Avon and Somerset constabulary, whose men and women have delivered so much in partnership with the police authority. I am sad to leave and stunned by the many messages of support I have received overnight from police officers and staff, Acpo [Association of Chief Police Officers], colleagues, partners and friends of Avon and Somerset Constabulary. To all of them, I say thank you."

Privately, Port is believed to be sceptical of the role of the PCC and over the last few months many within the force have suspected that he would not carry on after January.

Port's resignation may re-ignite the debate over the government's move to replace the old police authorities with an elected commissioner. David Cameron suffered a humiliating blow when his plans to democratise the police were met by overwhelming voter indifference, with the lowest ever turnout in a national poll.

More than a quarter of the new PCCs are having to recruit new chief constables. Some of those who left have done so because they did not want to serve under a commissioner.

Just before the elections, the acting chief constable of Gloucestershire police Mick Matthews resigned to take up a post in Cyprus. The force's previous chief Tony Melville had stepped down because of "grave concerns" over PCCs.

Mountstevens paid tribute to the work Port had done in Avon and Somerset, saying: " Colin Port has made great improvements for this area. He has increased detection rates and reduced crime. He will be greatly missed by staff and partners.

"Everyone is aware that the chief constable's contract expires on January 26. Because of that I would like to run a competitive process to appoint a chief constable for my whole term of office. It was his choice not to apply but I know that he will continue to do great things and I wish him the very best for the future."

The deputy chief constable, Rob Beckley, will act up as chief constable while the recruitment process is run.

Mountstevens is a 57-year-old former magistrate and former director of her family's bakery company in Bristol. She was – to many – the surprise winner in the election, beating a senior Tory Somerset county councillor, Ken Maddock, into second place.

She said her three main priorities were antisocial behaviour, violent crime, particularly against women and girls, and to listen, "especially to the quiet people".