From Longman Dictionary of Contemporary Englishkeep your eyes/ears openkeep your eyes/ears openNOTICEto keep looking or listening so that you will notice anything that is important, dangerous etc → open
Examples from the Corpus
keep your eyes/ears open• All of you - walk around Pentonville and keep your ears open.• Go back to bed only when you can no longer keep your eyes Open.• Swing the boat south, keep her eyes open.• The daily firings produced by the withering economy offered loopholes of opportunity for a young man who kept his eyes open.• The basic rules of self-defence are quite simple: keep your eyes open and you can usually avoid trouble.• You know how to keep your eyes open and your mouth shut.• Remembering his duty, he strode briskly up the stairs, keeping his eyes open for any suspicious signs.• By then keeping her eyes open was less of an effort. 