Ulster Unionist Party leader Steve Aiken said there has been a "definite failure" in policing in Northern Ireland, particularly at the most senior level.
Speaking on RTÉ's Morning Ireland, he said this means that the Chief Constable Simon Byrne has now lost the confidence of the unionist community, and many others across Northern Ireland, and it is time for him to go.
The UUP has joined other unionist parties in calling for the resignation of Mr Byrne over the handling of the funeral of senior republican Bobby Storey last summer.
Mr Aiken said the UUP "resolutely support" the PSNI, especially rank and file officers.
"Our support for the PSNI does not change", he said. "Our concern has been, and unfortunately has been for a while, the senior leadership of the PSNI, and in particular that role of the Chief Constable."
He said they decided to wait and hear what the Chief Constable said at the Policing Board yesterday.
He questioned how Simon Byrne "did not see" that the events surrounding Bobby Storey's funeral were breaches of health regulations.
"The problem is at the top and we can't wait any longer", Mr Aiken said. "The Chief Constable must consider his position."
It emerged yesterday that an independent agency is to be asked to examine the police handling of the funeral of Bobby Storey.
The PSNI has been strongly criticised after prosecutors said one of the reasons 24 Sinn Féin members who attended the funeral were not charged with breaches of Covid-19 restrictions, was because of engagement between organisers and police.
Northern Ireland's First Minister and DUP leader Arlene Foster has accused the police of facilitating the breaking of the law and called on Mr Byrne to resign.
Mr Byrne has rejected that call and insists that his officers acted appropriately.
He met his employers, the Northern Ireland Policing Board, virtually yesterday. Sources at the meeting said he "came out fighting" and made clear his intention to remain in post.
