nose out这个词组是把 nose 当动词，表示打探出；查出；嗅出，可以想成像警犬一样嗅出各种线索。

【例句】
The detective soon nosed out the details of the murder by talking to the people involved in it.
这名侦探和当事人们聊了聊后，他很快就打探出了谋杀案的细节。

They could come to terms, if you would keep your nose out.
他们会和好如初的，只要你不干涉。