Diagonal hairlines running up from the corners of door frames are really common, and they're usually not a structural worry. Door openings are a weak point: the lintel and frame move a tiny bit with temperature and humidity, and a rigid skim cracks along the line of least resistance. Seeing it...
Easiest way is to treat it like any other internal corner. Where the new wall's coving meets the existing run at 90 degrees, you cut a mitre on each piece: the new piece on the end of the wall and the existing coving where the new wall meets it. Because your new wall butts into the old coving...