。
I'm certain she'll succeed in her new job.
Literal
She [topic-は] this-coming work [at-で] succeed [quotative-と] I [topic-は] convinced am.
The sentence has two topics — 彼女は (the success) and 私は (the certainty) — splitting the embedded clause's subject from the matrix-clause subject. Without that split, 私は could be misread as the subject of 成功する. The quotative と packages the embedded clause '彼女は…成功する' as the content of conviction. 確信している is in the resulting-state ~ている: 'I am in a state of having become convinced,' not 'I am in the act of convicting myself.' Many mental-state verbs in Japanese use the ~ている form to describe ongoing belief: 信じている, 思っている, 知っている.