How to apply Custom Transform Orientation as a Local Transform I've created a custom Transform Orientation (named Side). I also have an object A in which the Local Transform Orientation is set to Global Transform Orientation. I want object A's Local Transform Orientation to be equal to Sides Orientation. How do I do that?
I would prefer a manual solution, but one using Python would work too.

I did some digging and found that You can set Transform Orientation in bpy.context.screen.areas[?].spaces[0].transform_orientation but it is just an enum with the name of a active transform. Where is the quaternion stored?
As I discovered while working on Blender function to transform a selected edge along a custom axis the transforms are stored in bpy.context.scene.orientations[i].matrix.  You can use orientations[0] or orientations[name].

If you want the rotation component as a quaternion use orientations[i].matrix.to_quaternion() .