A "stern look" refers to a facial expression that shows seriousness or disapproval. It is a look characterized by a serious, firm, and intense gaze, often used to convey a message or show dissatisfaction. Full definition
Checks however revealed that the business has been closed down with stern looking military personnel being mounted at the entrance of the hotel. (nigeriapoliticsonline.com)
Our pointer certainly gave me a pretty stern look as I squashed her in with the bags of pressies for the haul down to South Wales for some New Year festivities. (evo.co.uk)
But if it looks at you directly as if gazing at you with a very stern look, you might as well back off as this dog is usually tense. (mypetneedsthat.com)