She was getting nervous as the entrance exam approached.
Literal
She [topic-は] entrance-exam [object-を] [with-coming-up-控えて] nervous became.
~を控えて ('with ~ ahead, on the eve of ~') is a near-synonym of ~を前にして. 控える originally means 'hold back, refrain' but in this idiomatic use carries the sense of having something queued up just ahead.