Is this Prayer of Quiet, this supernatural way of prayer, able to be striven after or is it a gift? Both. The prayer itself is the gift of Jesus, the gift of living water (John 4), that enlarges our heart from within. St Teresa says: "however hard we strive, can we acquire it." This early form of contemplation is not the highest form of union, but it is "the purest gold of Divine Wisdom."
If we cannot acquire this supernatural prayer by striving, why does she tell her sisters you will "desire to strive to attain this way of prayer, and you will be right to do so"? She will answer this question as she goes along. But up to this point in the book, what can we say?
To have this gift in any kind of regular way, we need a basin. We need, that is, to be solid and shaped as God wants us to be. We need to be obedient. We need to be humble. We need to practice fraternal charity. Strive after these things and we will be striving after this higher way of prayer. Above all, strive by desiring, by asking for it.