From Longman Dictionary of Contemporary Englishstare somebody out British English, stare somebody down American English phrasal verbLOOK ATto look at someone for so long that they start to feel uncomfortable and look away → stare→ See Verb table
Examples from the Corpus
stare out• He sits facing the viewer, and staring straight out.• If looks could kill ... I tried to stare him out.• Some of the press read into that that I was trying to stare him out!• Tyrone Willingham said, staring sedately out at a group of reporters.• On the top floor of 32, Mrs Mackintosh stared nervously out at the dark street.• Luther stared at him out of terrified eyes.• The Marines were staring morosely out to sea, when a glimmer of unusual movement caught their eyes.• She was sitting beside him now, staring straight out towards the sea. 