allout-structure-shifted-hook is a variable defined in `allout.el'.
Its value is

Abnormal hook run after shifting items in an Allout outline.
Functions on the hook should take two arguments:

- DEPTH-CHANGE -- integer indicating depth increase, negative for decrease
- START -- integer indicating the start point of the shifted parent item.

Some edits that shift items can be missed by this hook: specifically edits
that native allout routines do not control.

This hook might be invoked multiple times by a single command.

You can customize this variable.