Liberal Democrat group leader Cllr Keith Aspden is to return as deputy council leader in March following a standards investigation.
The standards committee ruled that he did not bring the council into disrepute.
But councillors raised concerns that he had been involved in a discussion about job applications in a pub and they said this was a breach of the code of conduct.
The council confirmed that more than £84,000 was spent on external investigators.
The Liberal Democrats say they will now make a formal complaint to the council to “seek reassurances, question the level of council taxpayers’ money spent, raise administrative and procedural queries and demand urgent improvements”.
A spokesperson for City of York Council said: “We accept this has been an extremely complex and sensitive matter and we appreciate that this has been difficult for all involved.
“We are considering any matters that arise from the Joint Standards Committee recommendations and any formal complaints we receive and will make any necessary changes and improvements.”
Cllr Andrew Waller has been serving as deputy council leader and a handover period will now begin. Cllr Waller will continue in his role as executive member for the environment.
Cllr Aspden thanked his family, friends and supporters, adding:
I have never had to deal with a process like this in my professional, council or personal life. I sincerely hope that lessons are learnt and improvements made.
He said he was “more determined than ever to ensure that residents and local communities across York receive good quality and efficient services from the council” once he returns as deputy leader.