。
She holds a very enviable position.
Literal
She [topic-は] very enviable position [as-に] is-attached.
地位につく ('attach oneself to a position') is the standard idiom for taking up a role or office. The ~ている form here freezes that movement into a state — 'has come to occupy and remains in that position.' うらやましい is the i-adjective relative of the verb うらやむ (to envy), describing the position itself rather than feelings about it.