。
She calmed herself before speaking.
Literal
She [topic-は] speak [before-前に] feelings [object-を] calmed.
前に (まえに) marks the temporal boundary — 'before' the action of speaking. 気を鎮める (きをしずめる, 'to calm one's feelings/nerves') is a set expression using 鎮める, a more literary choice than 落ち着ける for calming down. 気 here represents one's emotional state.