Carmelite nuns make their vow of obedience with these words: “I, Sister Jennifer of Jesus, desiring to live a life of allegiance to Jesus Christ, with my sisters as witnesses, into your hands, [mother prioress] vow to Almighty God forever chastity, poverty and obedience according to the Rule and Constitutions of the Discalced Nuns of the Order of the Blessed Virgin Mary of Mount Carmel.” According to the approved Constitutions, obedience is rendered to the prioress when she commands according to the Rule and Constitutions. The obligation of observing canonical enclosure according to the Church document Verbi Sponsa (Spouse of the Word): Instruction on the Contemplative Life and on the Enclosure of Nuns is included in both of the approved Constitutions.
It seems worthwhile here to quote directly from this beautiful document, which was promulgated by Pope Saint John Paul II on May 13th, in 1999:
“The Holy Father Pope John Paul II has often exhorted nuns to remain faithful to the cloistered life in keeping with their particular charism; and in the Post-Synodal Apostolic Exhortation Vita Consecrata he decreed that to this end specific norms be given for the practical regulation of enclosure, continuing the path of renewal already undertaken, so that it may better suit the range of contemplative Institutes and the various monastic traditions. Thus, reborn of the Holy Spirit and faithful to their character and mission, cloistered nuns may move into the future with genuine momentum and renewed vigor… (Verbi Sponsa: Introduction 2).”