Maltese Auxiliary Bishop Charles Scicluna, who has being investigating clerical abuse for a decade, will visit Scotland next week to take testimonies from those with information about sexual misconduct surrounding the Cardinal.
Wider allegations will also be investigated.
In a letter to clergy in the Archdiocese of St Andrews and Edinburgh, Cardinal O'Brien's successor Archbishop Leo Cushley said Bishop Scicluna would "listen to and report the testimony offered by past and present members of the clergy ... concerning any incidents of sexual misconduct committed against them by other members of the clergy whomsoever".
Cardinal O'Brien stepped down as Archbishop of St Andrews and Edinburgh in February 2013 after he acknowledged sexual behaviour spanning his time as a priest, bishop and cardinal.
The move is a clear indication Pope Francis has not allowed the matter to drift.
According to Archbishop Cushley, Bishop Scicluna will visit the archdiocese between April 8 and 10 and "will be available to listen" on those days.
The Maltese bishop, Archbishop Cushley said, had also asked those who wish to speak with him to "prepare their narrative in writing".
Bishop Scicluna is best known in religious circles for being asked by then-Cardinal Joseph Ratzinger in 2005 to collect testimony regarding the serial sexual abuser and founder of the Legionaries of Christ, Fr. Marcial Maciel.
He served as the promoter of justice at the Vatican's Congregation for the Doctrine of the Faith until 2012, when he was made auxiliary bishop in Malta.
At the Vatican post he was known for reviewing hundreds of case files of priests who were eventually dismissed from ministry for sexual abuse.