。
She kept working at the bank.
Literal
She [topic-は] bank [at-に] continued-working.
勤める ('to be employed at, work for') takes its workplace with に — a common Japanese pattern where the place of long-term affiliation gets に rather than で. (で would be where an individual action happens; に is where one is anchored.) The compound 勤め続ける fuses 勤める ('work for') with the auxiliary ~続ける ('to keep doing'), yielding 'to keep working at.' Long tenure at a single company has historically been a Japanese workplace norm — the 終身雇用 (lifetime employment) tradition, although it's eroded since the 1990s, still shapes how this verb resonates.