I would take a picture showing the surrounding area. Hard to tell what is going on so close up and without any additional details.

Is that stucco, paint, concrete, exterior or interior, above or below grade?

Looks like an interior wall with sheet rock that is cracked and shifted not too far from the ceiling. If that is the case I would contact a structural engineer and see what they can discover.

" On my wall" What wall, what surface ? Drywall? A solid surface fireplace? Dark paint splitting apaprt? What? Nobody can tell ANYTHING from one dark picture, and no information.

No idea who to call to figure out what is happening w our recently bought house.

You start by getting a ladder, crawl up it with a stiff putty knife and chip away some of the material where the crack is. To determine whether this is a surface crack or if it extends through the substrate (drywall, plaster, etc.)

I suspect that this is either a plaster coat that has cracked because of minor house settling. Or too thickly applied drywall mud/ skim coat over previously finished/ textured/ painted surface.

Construction--frame, block wall?, age of house, geographic location, climate, etc. all relevant and not included in the original post. Also, interior wall of interior side of exterior wall? Roof trusses or stick framed? Ground level with attic above? Ground level with floors above? One small close up photo isn't sufficient. More, better photos needed but preferably eyes on local inspection.

Who to call? Experienced painting contractor and/or drywall contractor. Either should be able to diagnose if you cannot after a bit of investigation.