The most common and most likely answer to this crossword clue is the 5 plus 4 plus 4 letter word THREE YEAR OLDS
I've seen this crossword clue in Financial Times
T
H
R
E
E
Y
E
A
R
O
L
D
S
Buddy explains!
The straight part
We know that "one of these running in the Derby" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one of these running in the derby = three year olds.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.