The way how to get notifications whenever active object is changed in Blender.

active_was_changed.py

import bpy

owner = object()

subscribe_to = (bpy.types.LayerObjects, 'active')


def msgbus_callback(*args):
    print("Active object is changed!", args)


bpy.msgbus.subscribe_rna(
    key=subscribe_to,
    owner=owner,
    args=(1, 2, 3),
    notify=msgbus_callback,
)