In the New Testament there are various places which implicitly refer to the existence of judgement right after death. In the Parable of Lazarus and the Rich Man (St. Luke 16:22-31) the two men are taken to their respective places, bosom of Abraham and Hell, while the brothers of the condemned person are still alive. Further Christ says to St. Dismas, the penitent thief, that he will be with Him in Paradise on that very day (St. Luke 23:43) and according to St. Peter in the Acts of the Apostles, the suicidal Judas has “gone to the place which belonged to him” (Acts 1:25).
As to Holy Tradition, the Second Council of Lyons (1272-1274) and the Council of Florence (1431–1449) teach that people whose souls are completely clean from sin, either through baptismal innocence or otherwise, are immediately received into Heaven while those in mortal sin are directly condemned to Hell.
The Second Council of Lyons (D 464):
However, the souls of those who after having received holy baptism have incurred no stain of sin whatever, also those souls who, after contracting the stain of sin, either while remaining in their bodies or being divested of them, have been cleansed, as we have said above, are received immediately into heaven. The souls of those who die in mortal sin or with original sin only, however, immediately descend to hell, yet to be punished with different punishments.
The Council of Florence (D 693):
And that the souls of those, who after the reception of baptism have incurred no stain of sin at all, and also those, who after the contraction of the stain of sin whether in their bodies, or when released from the same bodies, as we have said before, are purged, are immediately received into heaven, and see clearly the one and triune God Himself just as He is, yet according to the diversity of merits, one more perfectly than another. Moreover, the souls of those who depart in actual mortal sin or in original sin only, descend immediately into hell but to undergo punishments of different kinds.