On hearing the news, she looked frightened.

Literal

She [topic-は] that news [object-を] hearing [then-て] being-frightened appeared.

おびえる ('to be frightened, be scared') is a verb for the inner state of fright — distinct from 怖がる ('act afraid'), which describes the visible behavior of fear. The te-form おびえて + 見えた gives 'looked-as-if-frightened' — a third-person observation, not a direct claim about her feelings. This ~て見える pattern lets the speaker hedge: she looked scared, though I can't know for sure. Useful for narrating other people's emotional states without overclaiming.