I believe you mean the phrase, “out of fear,” or “for/in fear of.” These two phrases generally refers to the action or reaction of a person when he or she is scared into doing something.
For instance; “Kyle hid his face from the lion out of fear of being bitten.”
“Julie walked quickly for fear of being discovered.”
“Thousands of people are in fear of their lives following the shootings.”
“Ordinary people lived in fear of being arrested by the secret police.”
“She finally ran away for fear that he would kill her.”
“He got to the station early, for fear of missing her.”
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