### 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, state: DagRunState | None = None, session: Session = NEW_SESSION
    ) -> pendulum.DateTime | None:
        """
        Return the start date from property previous_ti_success.
        :param state: If passed, it only take into account instances of a specific state.
        :param session: SQLAlchemy ORM Session
        """
        self.log.debug("previous_start_date was called")
        prev_ti = self.get_previous_ti(state=state, session=session)
        
        return prev_ti and prev_ti.start_date and pendulum.instance(prev_ti.start_date)
    @property
    def previous_start_date_success(self) -> pendulum.DateTime | None:
        """
        This attribute is deprecated.
        Please use :class:`airflow.models.taskinstance.TaskInstance.get_previous_start_date`.
        """
        warnings.warn(
            """
            This attribute is deprecated.
            Please use `airflow.models.taskinstance.TaskInstance.get_previous_start_date` method.
            """,
            RemovedInAirflow3Warning,
            stacklevel=2,
        )
        return self.get_previous_start_date(state=DagRunState.SUCCESS)
    @provide_session
    def are_dependencies_met(