。
She took a position of responsibility at the company.
Literal
She [topic-は] company [of-の] responsibility have position [in-に] took-up.
地位につく is a set phrase: 地位 ('position, status') + 付く ('attach to, take up') = 'take up a (job/social) position, assume a post.' The 責任ある is the noun-modifying phrase 'having responsibility' (relative clause built around ある with 責任 as its の-marked subject), so 責任ある地位 = 'a position with responsibility.' The に here marks the destination of the action — 'into the position' — typical of つく's pattern.