Dunleavy was found guilty of 36 charges of historical sexual abuse against nine boys last year.
He was later sentenced to ten years behind bars for a series of offences that included indecent assault and gross indecency with or towards a child.
The crimes were committed between 1964 and 1991 while Dunleavy worked at four schools in Belfast, Newry and Armagh.
The victims were aged between seven and 14 at the time.
Dunleavy was already serving a sentence after he was previously convicted on two separate occasions of sexual offences against children.
His latest prison term will commence at the end of his current sentence in May next year.
The predator has been convicted of 72 sexual abuse offences involving 18 victims over a 28-year period ending in 1991.
A letter of claim was last year issued to solicitors representing the Congregation of Christian Brothers on behalf of 16 people targeted by Dunleavy.
Owen Beattie, of Owen Beattie Solicitors, who represents several of Dunleavy’s victims, has previously written to senior Christian Brother officials.
The solicitor has now raised fresh concerns in a recent letter to the order, which has also been sent to Archbishop Eamon Martin.
“The continued membership of Brother Paul Dunleavy within the Christian Brothers is extremely concerning,” he said.
“Dunleavy has been convicted of sex offences on children which he perpetrated on an industrial scale.”
Mr Beattie added that Dunleavy “used the Chrisitian Brothers as vehicle to enable his predatory behaviour, yet they as an organisation have not removed his membership”.
“The failure on the part of the Christian Brothers to take any meaningful steps to address these wrongs, only seeks to cause further trauma,” he said.
“The outworkings of this questionable conduct will be factored into our ongoing civil actions before High Court on behalf of our clients.”
The Christian Brothers were contacted.