Welcome to the Airtable community!
This feature does not exist and is unlikely to ever exist. Airtable rows are unaware of their relative positioning and thus cannot take action based on changes to row order. A change in row order is not a data change. This is in part because records can appear in different orders in different views.
If you can identify the specific data change that causes a record to change position, you might be able to run an automation that updates a field in all affected records. This would likely require scripting.