No, Celery Beat knows nothing about the running tasks.
One way to achieve what you are trying to do is to link the task to itself. async_apply() for an example has optional parameter link
and link_error
which can be used to provide a signature (it can be a single task too) to run if the task finishes successfully (link) or unsuccessfully (link_error).
What I use is the following - I schedule task to run frequently (say every 5 minutes), and I use a distributed lock to make sure I always have only one instance of the task running.
Finally a reminder - you can always implement your own scheduler, and use it in your beat configuration. I was thinking about doing this in the past for exactly the same thing you want, but decided that the solution I already have is good enough for me.