English Idiom

>keep an eye on
Meaning
If you keep an eye on

someone, you make sure you know what they're doing.
For example
🔸I'm a bit worried about Hannah's health so could you keep an eye on her while I'm away?

🔸Mom asked me to keep an eye on my little sister while she went to the supermarket.
Note
You can also say "keep my eye on", "keep your eye on" etc., as in "I asked Mary to keep her eye on that dog."