Sentence examples for for a run from inspiring English sources

The phrase "for a run" is correct and can be used in written English.
It is typically used to indicate the purpose or reason for doing a particular activity or action. Example: I woke up early this morning for a run around the park. In this sentence, the phrase "for a run" explains why the person woke up early in the morning. Another example: She went to the gym for a run on the treadmill. Here, "for a run" explains the activity the person engaged in at the gym.