Indeed. The design for what happens in which thread needs to be thought
through, taking into account the rules about what can wait for what.

Let's give the entities involved some names:

As I understand the problem, thread A spawns thread B to run task X, and
then itself does task Y. Task Y must not start until task X completes.
Because of other responsibilities, thread A cannot wait for task X to
complete.

In that case, thread A cannot be the thread that runs task Y.

The easiest way to ensure that Y does not start until X finishes is
still to have one thread do both of them, in the proper order. How about
having thread B do task X followed by task Y?

Patricia