The most common and most likely answer to this crossword clue is the 13 letter word SUPERINTENDED
S
U
P
E
R
I
N
T
E
N
D
E
D
Buddy explains!
The straight part
We know that "Kept an eye on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kept an eye on = superintended.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 SUPERINTENDED mean?
SUPERINTENDED verb- To oversee the work of others; to supervise.
- To administer the affairs of something or someone.