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She has no choice but to give up smoking.
Literal
She [topic-は] cigarettes [object-を] stop [have-no-choice-but-to-ざるをえない].
~ざるを得ない is a literary double-negative pattern — built from the classical negative attributive ざる (the older form of ない) plus 得ない ('can't get'). Roughly: 'cannot get away without doing X' = 'have no choice but to X.' It's noticeably more formal than the everyday alternative ~しかない. Productive with most verbs: 認めざるを得ない ('have to admit'), 行かざるを得ない ('have to go'). Note 止める here is read やめる ('quit, stop'), not とめる ('halt'). The choice of literary phrasing lends the sentence a slightly weighty or reluctant feel, fitting the topic of forced behavior change.