Bishop Stephen Robson, who was installed at St Andrew's Cathedral in Dundee last week, said it would be "gravely wrong" not to forgive the cardinal, who resigned as Archbishop of St Andrew's and Edinburgh last year after admitting to inappropriate behaviour.
However, he said the churchman needed to make reparation for the harm he had done.
Bishop Robson, who was an Auxiliary Bishop to Cardinal O'Brien, told Catholic newspaper The Tablet: "Never once in all that time did I experience anything of the behaviour he was accused of. That is why his downfall came as such a shock to me and to so many. The Cardinal was much loved in the archdiocese.
"I was a bishop only a few months when this sad narrative began to unravel. The cardinal admitted behaviour unbecoming in a man of God and I do not believe forgiveness of him is at question."
Bishop Robson took over his position from Vincent Logan, who stood down more than three years ago. His new appointment covers the Dundee and Tayside area.