Keep your pull request up to date with their base branch.
You can either use the branch protection in your repository or write finer-grained conditions in your Mergify configuration. Define which checks are mandatory, the number of reviews required, etc, to get a pull request mergeable.
Mergify updates the pull request status in real-time and informs you about which criteria match. As soon as your condition is validated, Mergify makes sure the pull request is up-to-date with its base branch.
If not, it updates it by rebasing it or merging the base branch in it, waits for the merge condition to match again (e.g., CI passing), and finally merges it. Automatically.