Newport West MP Paul Flynn says the row over the forcing out of the former Gwent Chief Constable by the force's Police and Crime Commissioner shows "it is the system that is wrong - it's going to happen elsewhere too."
He said the problem is "two people thought they were running the police force".
Ms Napier has called on the UK government to consider whether the independence of operational policing could be compromised by the power given to PCCs.
Carmel Napier has issued a statement in which she says "the timing of her retirement was not of her choosing.
The former Gwent Chief Constable says the government must consider whether legislation around the powers of Police and Crime Commissioners to call for chiefs to retire or resign "adequately protects the independence on operational policing."
Police and Crime Commissioners have a crucial role to play in representing the people the police serve and in ensuring chief constables are held to account for the quality of service they deliver in their communities.
Chief Constables up and down the country accept and support that. However, much has been made of the need for PCCs not to stray into areas of operational policing and how important it is for chief constables to retain that independence.
The government must consider whether the legislation governing the PCCs' power to call for chiefs to retire or resign adequately protects the independence of operational policing in England and Wales.
– Carmel Napier, former Gwent Police Chief Contable