。
She was shut out of the club.
Literal
She [topic-は] that club [from-から] was-shut-out.
締め出される is the passive of 締め出す, a compound verb pairing 締める ('tighten, close, fasten') with 出す ('put out'), giving 'shut out, lock out'. The image is of the door being closed against someone — physical exclusion crystallized as a single verb. から marks the source/origin one is being excluded from. Compound verbs with ~出す productively cover all kinds of 'out'-actions: 追い出す ('drive out'), 持ち出す ('carry out'), 取り出す ('take out'). Together with the passive, the phrase paints a picture of being unceremoniously locked out without further explanation.