Below are the only known references to the Law of Destiny in the writings of Alice A. Bailey (AAB) and Djwhal Khul (DK). Links on these pages of the Laws of Alice A. Bailey are to the online books at the Lucis Trust website.
For a discussion of what AAB means by a “law” please see Alice A. Bailey – What is a Law?
What we are dealing with here, in connection with initiate training, is the impending realisation for which any opening cycle attests its waiting, and for the new truths and the expanded spiritual presentations which it is the destiny of the initiate to bring to the people. You will note that I choose the word “destiny” in preference to the word “karma” because in this type of work the initiate is working and practising and progressing under a Law of Destiny.
This law affects the Ashram and the Hierarchy as a whole, and neither  is under the Law of Karma, as usually understood. This Law of Destiny has been brought into being since the foundation of the Hierarchy on Earth; it is the result of the pledged and united dedication to service which is the outstanding note of the united Ashrams.
Theosophist William Q. Judge wrote that:
“… each man is the maker and fashioner of his own destiny, the only one who sets in motion the causes for his own happiness and misery. In one life he sows and in the next he reaps.” -The Ocean of Theosophy, Theosophical University Press Online Edition
Lee Bladon on his website esotericscience.org writes of the Law of Destiny:
“The law of destiny determines what forces influence our lives to ensure we encounter the life experiences that we require for our continued development. Destiny is essentially a series of opportunities that enable us to learn lessons, acquire new abilities, develop our consciousness and help others.” -Destiny, Karma and the Law of Attraction
You are welcome to post your comments and understanding of this law.