。
She had been quiet the whole time.
Literal
She [topic-は] the-whole-time quiet [adverbial-に] was-doing.
静かにする ('be / stay quiet') is built from 静か (na-adjective 'quiet') + に (the adverbializer for na-adjectives) + する ('do'). The combination is the standard way to say 'maintain silence as an active behavior'; teachers say 静かにしてください ('please be quiet') in classrooms, parents say 静かにしなさい to children. Past progressive 静かにしていた describes that ongoing maintained behavior over a stretch of time. Pair with ずっと ('the whole time') and the duration becomes explicit.