The BBC's Panorama broadcast evidence of abuse at the Medway Secure Training Centre (STC) in Rochester in January.
Four men were arrested on suspicion of child neglect while a fifth was held on suspicion of assault. All were bailed.
East Sussex County Council said a young person placed at the STC since the documentary aired made the allegations.
The revelation was made in a report to be considered on Friday by the council's corporate parenting panel - which monitors and ensures the wellbeing of children who are looked after by the authority.
The report said there was just one young person from East Sussex placed in the G4S-run Medway STC during the period in which the filming for the programme took place.
"This young person was not involved in any of the incidents and has been asked explicitly but has not reported any concerns.
"Another young person from East Sussex has made allegations since the programme has been aired."
Councillors said the latest allegations were being investigated through the Local Authority Designated Officer (LADO) in Medway and via the police.
East Sussex Children's Services and its youth offending teams had supported the investigation, the council said.
In a statement, Kent Police said "further allegations" had been received and were being investigated.
The Panorama programme included footage apparently showing staff mistreating and abusing inmates.
Allegations relating to 10 boys, aged 14 to 17, included use of unnecessary force, foul language and a cover-up at the centre.
Five members of staff were sacked and three more suspended, while the unit's director, Ralph Marchant, stood down.
The unit takes 12-to-17-year-old youths, both on remand and after conviction.
Further allegations relating to a young offenders' unit at the centre of claims staff assaulted children are being investigated by Kent Police.