An independent panel said Wiltshire Police will be in a "precarious situation" without a police and crime commissioner (PCC) at its helm.
Jonathon Seed was voted into the role for Wiltshire Police in May but was unable to take the position due to a historical driving conviction.
Without a PCC, no one has authority to fire or hire the Chief Constable.
Chief executive of the office of police commissioner Kieran Kilgallen will be made an interim PCC until 19 August.
Conservative Party candidate Mr Seed received 40% of the vote in the first round and was elected after it went to a second ballot.
However, the party said Mr Seed, who had been hoping to take over from departing Conservative colleague Angus Macpherson, had been "disbarred" after a driving offence had "come to light".
Electoral Commission guidance states candidates for police and crime commissioner posts cannot stand for election if they have been convicted of an offence punishable with a prison sentence.
In a meeting addressing how the force will be run until a new PCC is elected, senior figures were questioned by the police and crime panel, a group of Swindon and Wiltshire councillors who are tasked with scrutinising the force.
Chairman Junab Ali said without a PCC things that need to be signed off will have to be put on hold.
He said: "We are in a really precarious situation, so I think all of us will be learning and we have to be very patient as we go along to find a way through this impasse."
Talking about a scenario whereby there was a gross misconduct case involving a Chief Constable and a requirement for an approved authority, Mr Kilgallen told the meeting: "I am quite confident that in the next three months we will avoid any need for an approved authority."
Thames Valley Police has launched an investigation into the circumstances surrounding the election.
Analysis: BBC Radio Wiltshire Political Reporter Dan O'Brien
The meeting did shine a light on how the force has been functioning since May's election failed to deliver a commissioner.
Wiltshire's previous PCC Angus Macpherson delegated some extra powers to senior officials.
This means senior unelected officials can sign off on deals which normally would need the Commissioner's approval, such as the force's contracts for IT, Victim Support and the Sexual Assault Referral Centre which are up for renewal.
But they won't be able to take decisions over the proposed sale of some rural police stations like Calne's.