The most common and most likely answer to this crossword clue is the 8 letter word OVERSEES
I've seen this crossword clue in The Times
O
V
E
R
S
E
E
S
More clues leading to the result OVERSEES
Buddy explains!

The straight part
We know that "Keeps an eye on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case keeps an eye on = oversees.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does OVERSEES mean?
OVERSEES verb- To survey, look at something in a wide angle.
- To supervise, guide, review or direct the actions of a person or group.
- To inspect, examine
- To fail to see; to overlook, ignore.
- To observe secretly or unintentionally.