Hello E Glynn.
A member of a religious order leaving it to start a new order can, and does, occur. Naturally, this sort of thing should happen after a period of prayerful discernment as well as under the direction of one’s religious superiors and the proper ecclesiastical authorities. A good example of someone doing this in the modern era is Blessed Teresa of Calcutta (a.k.a., Mother Teresa). She initially joined the Sisters of Loretto but later left to establish the Missionaries of Charity. As a side note, there can be nuances in how a religious community is specifically identified and designated, so I am simply using the term “religious order” in a general sense.
