The Monastery of a cloistered heart is the person's own life. A monastery is a place consecrated to God, a place of prayer, a place where God is loved and served. Our lives can be all of these things. Just as any building can become a monastery by being dedicated to God, so our lives can become "monasteries" by such dedication.
This is more than a nice daydream. It is simply truth.
"Even now we are called to be a dwelling
for the Most Holy Trinity. 'If a man loves Me,' says the Lord, 'he
will keep My word, and my Father will love him, and we will come to him,
and make our home with him.' (John 14:23)" (Catechism of the Catholic
"O my God.... grant my soul peace. Make
it Your heaven, Your beloved dwelling, and Your place of rest. May I
never abandon You there, but may I be there, whole and entire,
completely vigilant in my faith, entirely adoring, and wholly given over
to Your creative action." (St. Elizabeth of the Trinity)
As imperfect as we are, Our Lord actually desires to
live within us.
Painting: Fritz von Wille, in US public domain due to age