From Longman Dictionary of Contemporary Englishkeep a sharp eye on somebodykeep a sharp eye on somebodyWATCHto watch someone very carefully, especially because you do not trust them Keep a sharp eye on the kids at all times! → sharp
Examples from the Corpus
keep a sharp eye on somebody• I keep a sharp eye on him.• Security guards kept a sharp eye on Mattson as he walked through the store.• As a teen-ager, I kept a sharp eye on who was winning the prizes I wanted: Honor Roll. 