How do I repair cracks in thincoat plaster?
That crack is most likely directly inline with a seam between two sections of the underlying drywall. Environmental effects or settling of the building structure over years can lead to cracks like this opening up.

Probably the best fix for this is to sand to roughen up the area for six to eight inches or so on either side of the crack. Then apply some good quality mesh style drywall joint tape:



(I would actually install in two overlapping layers).

Then use a drywall mud knife to embed the tape into a layer of drywall mud that is feathered out over a wide area on either side of the mesh tape. If the drywall mud is installed carefully over multiple applications you can minimize the amount of sanding required.