You could get clues by looking at other actions on how to achieve that.
For example, here is an action that changes the tasks color when the due date is reached, you would just need to modify it to move the task instead.
and this one would show you how to actually move the task:
followed by the docs that would show you how to turn your new action into a plugin:
I think that should give you every bit of assistance you need to do this yourself. If you need a plumber though, I’m happy to help.