。
She turned pale upon hearing the bad news.
Literal
She [topic-は] that bad news [object-を] heard-and pale became.
青くなる ('to turn blue') is one of several Japanese color metaphors for emotional or physiological state: 青 ('blue') stands in for 'pale, ashen' when describing a face drained by shock, fear, or illness — Japanese has long lumped pale-bluish-pale-greenish hues together under 青. The face going blue describes the loss of color from sudden distress. Sister phrases include 真っ青になる ('go ghost-white'), 顔が青ざめる (same idea, more literary), 赤くなる ('blush red'). The te-form 聞いて chains hearing to reaction, marking cause-effect in a single tight clause.