I did exactly that. Much of my first few months with my current T were spent discussing my feelings for T1. This included unpicking the transference and coming to understand its roots, and why it occurred, but also simply mourning the loss of someone who was important to me and that I cared about.
The loss of T1 still resurfaces from time to time 9 months after starting with current T, but much of the uncomfortable transference has now been resolved through understanding.
I hope you can find some peace about the situation