Deputy Kirsten Morel had lodged a proposition calling for the process to be paused until after the June general election, to allow for the recommendations of a report by Comptroller and Auditor General Lynn Pamment on the appointment process to be implemented.
But in the States Assembly on Wednesday, Deputy Morel withdrew his proposition, saying it would be going against 'what is best for Jersey'.
It emerged during the sitting that there would be legal consequences for the States Employment Board if the proposition was approved, with Solicitor General Matthew Jowitt saying it would drive 'a coach and horses through the law'.
Former chief executive Charlie Parker left his role earlier this year following controversy over his decision to accept a non-executive director’s role with a UK-based real estate firm, with interim chief executive Paul Martin replacing him.
The post has now been offered to Suzanne Wylie, who is currently in charge of Belfast City Council.
Once the position was offered and accepted by the candidate, Mr Jowitt said employment regulations meant a successful proposal would require the SEB to break the law.
He said: 'This proposition, I am bound to say - and it is the opinion of law officers - if adopted and acted upon by the SEB, would entail them calling an abrupt halt to a lawful and legally binding selection process.'
Mr Jowitt said the proposition could have led to a challenge in the Royal Court by way of judicial review.