A priest from Diocese X and a lay person travel by train to some place. During the trip the latter feels the need to confess sacramentally. The train at that moment is in Diocese Y, where the priest has no faculties to hear confessions. What is the way round? Call to the ordinary bishop?
No, the priest can hear the confession and validly absolve unless there are rare circumstances in play.
If Father has faculties to hear confessions in his own diocese or order, he can hear them everywhere except when specifically told that he can’t. If it is a matter of hearing confessions regularly in another diocese, then he needs to work that out with the local diocesan curia. But, the occasional confession here and there, on a legitimate (read: reasonable) request, when traveling – such as in an airport – good to go!
Ordination gives a priest the power to absolve, but not the permission to use the power.
To use the power validly – validly, mind you, not just licitly – he must have juridiction/permission/authority from the Church. This is his “faculty”. Faculties are granted by proper authority (such as the diocesan bishop or religious superior) or by the law in particular situations itself (such as danger of death).
Can. 967 §1 says that the law itself grants that cardinals can hear confessions everywhere. So can a bishop unless he has been forbidden to do so by the local bishop. So, if the priest on the train is Bishop Jude Noble of Black Duck, and the Bishop of Libville, Most Rev. Fatty McButterpants, hates the Bishop of Black Duck because he believes in God and the Church’s Holy Dogmas, and Fatty has told the noble Bishop of Black Duck in writing that he mayn’t hear confessions, you are out of luck. BUT, if the new Pope Pius XIII, before disappearing into the Apostolic Palace, made the Bishop of Black Duck a cardinal, then ol’ Fatty can go pound sand and the layman on the train can be validly absolved.
Can. 967 §2 says that those who possess the faculty of hearing confessions habitually (whether by virtue of office – he’s a parish pastor – or by virtue of the grant of an ordinary of the place of incardination or of the place in which they have a domicile) can exercise that faculty everywhere unless the local ordinary has denied it in a particular case (except in danger of death, of course). So, if Father Joe Włotrzewiszczykowycki of the Diocese of Libville, having fled the persecution of Bp. McButterpants for his belief in God and the Church’s Holy Dogmas, now has domicile and the faculties of Black Duck from Bp. Noble, he can absolve inside Black Duck, outside Black Duck, and still also in Libville.
During the Year of Mercy, even SSPX priests can validly absolve in such a situation. Please note that, if this is an Agatha Christie situation on a train, and the layperson is dying because of murder, in danger of death all priests have the faculty to absolve validly, even if the priest had been “laicized” for whatever reason (can. 966 §2). In such a case, the day after the Year of Mercy ends even an SSPX priest, call him Fr. Fidel Jose Maria del la Cruz, can validly absolve in danger of death. But if there is no danger of death, then Fr. Fidel – outside the Year of Mercy – won’t have the faculty validly to absolve.