You need to supply ‘area’ and ‘region’ context keys to override the operator from a different area.
import bpy
context = bpy.context
def show_active(context):
override = None
for area in context.screen.areas:
if 'OUTLINER' in area.type:
for region in area.regions:
if 'WINDOW' in region.type:
override = {'area': area, 'region': region}
break
break
if override is not None:
bpy.ops.outliner.show_active(override)
if '__main__' in __name__:
show_active(context)
You can turn this into a hotkey by saving to a py file and adding it using the blender operator script.python_file_run
in the hotkey editor.