COUNCIL bosses are to examine whether the authority needs a chief executive in the wake of Mr Reeves' departure, it has been revealed.
Opposition Conservative councillors are calling on the cash-strapped authority to axe the £178,000-a-year chief executive's post to save money.
Conservative leader Councillor Glen Miller said: "We do not believe there's a need for a chief executive when we have an overall-controlled council and policy is made by politicians."
But Council leader, Labour's Councillor David Green, said while the role would be reviewed, the authority would need a chief officer in some form.
He said: "We will be clearly looking at the structure of the Council before we make a decision on whether to re-appoint a chief executive or have a different form of head of the paid service, so we won't be leaping into making a decision.
"I look forward to hearing any sensible views regarding that."
Cllr Green added that the Labour control of the council was an entirely separate matter.
He said: "I have been in Bradford politics for long enough to know that isn't always necessarily going to be the case. You can't make decisions on the management of the council based on one election result."
And Liberal Democrat leader, Councillor Jeanette Sunderland, reacted with alarm at the thought of the chief executive not being replaced.
She said: "This is an organisation with a multi-billion-pound turnover. At a time when we need strong leadership, with high rates of unemployment and some real challenges to face, it would be foolish to think that politicians could run the district."