Father Brown is actually a Jesuit priest (Catholic, but belonging to the religious order of Jesuits). In that sense he does have a religious superior (Father Superior). In the later "The Three Tools of Death" he is introduced as Father Brown, S.J. (the religious order's initials).
Father Brown says, "Our Father Superior is constantly telling me I lack foresight." There is no such title in the hierarchy of the Catholic Church (unlike 'Mother Superior', which often designates the chief nun in a convent). The head of a religious community may be called the Superior (and Father Brown is a diocesan priest, so this doesn't apply; he would be answerable to his Bishop), and every priest may be called Father, but never the two together.