Only last week Councillor Hussey was installed as deputy mauor at the Guildhall.
He was the Ulster Unionist nominee to the post for the next twelve months which came before Thursday’s meeting of the council’s health and community committee.
The chair is rotated between the four largest parties on the council.
He was the only PCSP committee member of the fourth-largest UUP and council officials recommended Mr Hussey for the post.
But Sinn Fein councillor Eric McGinley said his party was not in a position to support the nomination.
“He has high-profile driving offences and road safety is an important matter in this role,” he said.
“We cannot support his position as chairman and that is not a reflection on his record as a member of the committee.”
Mr Hussey was given a five-year driving ban and fined £800 in 2016 after pleading guilty to drink-driving. He had previously been convicted of drink-driving offences in 2004 and 2011.
Council officers told the committee: “As the Ulster Unionist Party is the fourth largest party on the council and as Alderman Hussey is the sole UUP representative on the PCSP, it is recommended that Alderman Hussey is nominated to take the chair.
“Alderman Hussey will serve as chair of the PCSP until the reconstitution of the PCSP following the next local government election.”
Sinn Fein members did not contest the nomination, which was agreed by the committee and will go forward for ratification at the full meeting of the council at the end of the month.
The deputy mayor said: “I fully regret my actions which were dealt with by the courts.
“I will do my utmost to serve all members of the committee and the public as chair of the Policing and Community Safety Partnership.
“This will not affect my judgement as chair of the PCSP.”