Religious order priests go where their superiors send them. As for secular priests, before entering seminary a man might be able to petition the bishop of a diocese not his own to consider him for the priesthood, but a bishop is likely going to be wary of a man who is “fleeing his diocese.” That doesn’t mean that a bishop might not accept a man from another diocese into his own, only that such a man might be scrutinized more carefully. Perhaps a better solution would be for such a man who is discerning the secular priesthood to move to a diocese he thinks he would like and live as a lay Catholic there for a few years before approaching the bishop about a vocation to the priesthood. After ordination, of course, a secular priest is vowed to obedience to his own bishop and generally should not be casting his eyes afield for other dioceses.
