From Longman Dictionary of Contemporary Englishfasten your eyes/gaze on somebody/somethingfasten your eyes/gaze on somebody/somethingLOOK ATto look at someone or something for a long time He rose, his eyes still fastened on the piece of paper. → fasten
Examples from the Corpus
fasten your eyes/gaze on somebody/something• Maggie fastened her eyes on him and tried to get control of her temper and her very stupidly lingering disappointment. 