。
She was irritated from being kept waiting a long time.
Literal
She [topic-は] long waited-was-made [and-て] irritatedly was.
待たされて is the causative-passive of 待つ: 'was made to wait' — she didn't choose to wait, someone forced the waiting on her. This is followed by いらいらしていた, where いらいら is a 擬態語 (state mimetic) for the feeling of irritation or impatience. The causative-passive efficiently expresses both the external cause and the internal emotional response.