Maybe once the author finishes her latest work. We can only hope
Aji was originally hosted on Lezhin. However, the author left due to certain disputes. Each author contracted with Lezhin is basically signing over the rights to said story and it lasts for about five years. Now, I'm not sure exactly when this all happened, but I don't think those contractual years are up just yet. When they are, Aji will be free to continue this story. That said, Aji is busy with Opium and we won't know if they plan to continue On A Leash at least until after it's finished. At the very least.
Will this even update?