。
She turned pale with fear.
Literal
She [topic-は] fear [at-に] turned-pale.
The cause is marked here with に — distinct from のため (more explicit) or で (more matter-of-fact). The に in 恐怖に青ざめる is the 'cause/trigger of emotional reaction' — the same に in 雷に驚く ('be startled by thunder'), 病気に苦しむ ('suffer from illness'). It compresses the cause-and-effect tightly and lends a slightly more dramatic feel than the alternatives.