The most common and most likely answer to this crossword clue is the 3 plus 2 plus 6 letter word PUT TO FLIGHT
I've seen this crossword clue in The Times
P
U
T
T
O
F
L
I
G
H
T
Buddy explains!
The straight part
We know that "make to race away" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make to race away = put to flight.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.