A regular nurse is entitled to three weeks' vacation per year.

Literal

Normal nurse [topic-は], year [per-に] 3-weeks vacation [object-を] take right [subject-が] exists.

権利がある means 'to have the right to.' 看護婦 is an older term for 'nurse' (female); the gender-neutral 看護師 is now standard. 年に = 'per year.'