She let out a cry of fear.

Literal

She [topic-は] fear [genitive-の] scream [object-を] raised.

恐怖の叫び声 ('scream of fear') uses the genitive の to specify the kind of cry — built like English's 'cry of fear,' 'scream of pain.' 叫び声を上げる/あげる ('raise a scream') uses 上げる/あげる ('raise') as Japanese's verb of choice for vocal outbursts — 'raise' rather than 'release.' The pattern ~の[noun-of-vocalization] is productive: 喜びの声 ('voice of joy'), 怒りの叫び ('cry of anger').