She was angry, but she suppressed it and spoke.

Literal

She [topic-は] angry was [but-が] that [object-を] suppressed [and-て] talk [object-を] did.

それをおさえて ('suppressed that/it') refers back to the anger from the first clause. おさえる (抑える) means 'to suppress / hold down' — used for controlling emotions, urges, or reactions. The clause-final が works as a soft 'but,' and the て-form chains the suppression with the speaking. Shows emotional self-regulation — she chose to speak despite her anger.