### Discussed in https://github.com/apache/airflow/discussions/33345

<div type='discussions-op-text'>

<sup>Originally posted by **vuphamcs** August 11, 2023</sup>
### Description

Is there a variable similar to `prev_start_date_success` but for the previous DAG run’s completion date? The value I’m hoping to retrieve to use within the next DAG run is `2023-08-10 16:04:30`

![image](https://github.com/apache/airflow/assets/1600760/9e2af349-4c3e-47e1-8a1a-9d8827b56f57)


### Use case/motivation

One particular use case is to help guarantee that the next DAG run only queries data that was inserted during the existing DAG run, and not the past DAG run.

```python
prev_ts = context['prev_end_date_success']

sql = f"SELECT * FROM results WHERE created_at > {context['prev_end_date_success']}"
```

### Related issues

_No response_

### Are you willing to submit a PR?

- [ ] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)
</div>
self, dep_context: DepContext | None = None, session: Session = NEW_SESSION, verbose: bool = False
    ) -> bool:
        """
        Are all conditions met for this task instance to be run given the context for the dependencies.
        (e.g. a task instance being force run from the UI will ignore some dependencies).
        :param dep_context: The execution context that determines the dependencies that should be evaluated.
        :param session: database session
        :param verbose: whether log details on failed dependencies on info or debug log level
        """
        dep_context = dep_context or DepContext()
        failed = False
        verbose_aware_logger = self.log.info if verbose else self.log.debug
        for dep_status in self.get_failed_dep_statuses(dep_context=dep_context, session=session):
            failed = True
            verbose_aware_logger(
                "Dependencies not met for %s, dependency '%s' FAILED: %s",
                self,
                dep_status.dep_name,
                dep_status.reason,
            )
        if failed:
            return False
        verbose_aware_logger("Dependencies all met for dep_context=%s ti=%s", dep_context.description, self)
        return True
    @provide_session
    def get_failed_dep_statuses(self, dep_context: DepContext | None = None, session: Session = NEW_SESSION):