According to the official Airflow docs,
The task instances directly upstream from the task need to be in a success state. Also, if you have set de
From the official docs for trigger rules:
depends_on_past (boolean) when set to True, keeps a task from getting triggered if the previous schedule for the task hasn’t succeeded.
So unless a previous run of your DAG has failed, the depends_on_past should not be a factor, it will not affect the current run at all if the previous run executed the tasks successfully.