That’s sort of how the Orthodox Church works. While priests can’t marry, married men can become priests - and in fact men considering the priesthood are encouraged to marry, as a married priest is considered more able to give pastoral advice to couples about their marriage. There’s a reason why the most common surname in Greece, Papadopoulos, means “son of the priest”.
On the other hand, members of the church hierarchy (bishops and up) must be monks, and therefore can’t be married. So an unmarried Orthodox priest probably has ambitions…
