The most common and most likely answer to this crossword clue is the 4 plus 9 letter word DEAD CERTAINTY
I've seen this crossword clue in The Daily Telegraph
D
E
A
D
C
E
R
T
A
I
N
T
Y
More clues leading to the result DEAD CERTAINTY
Buddy explains!
The straight part
We know that "Racehorse that’s sure to have the most life, paradoxically" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case racehorse that’s sure to have the most life, paradoxically = dead certainty.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.