。
She hired a private detective to investigate the case.
Literal
She [topic-は] that case [object-を] investigate [for-のに] private-detective [object-を] hired.
~のに here is the purpose marker ('in order to / for the purpose of') — distinct from the 'despite' use of ~のに that appears with clause-final predicates. Recognizable because it follows a dictionary-form verb (調べる) at the front of the sentence, not a clause-final inflection. 私立探偵 ('private detective') is a Sino-Japanese compound that arrived through Japanese consumption of Western detective fiction; it's the standard term in pulp novels, manga, and TV mysteries. 雇う ('to hire, employ') takes the hired person as object.