The most common and most likely answer to this crossword clue is the 5 plus 8 letter word HEIRS APPARENT
I've seen this crossword clue in The Sunday Telegraph
H
E
I
R
S
A
P
P
A
R
E
N
T
More clues leading to the result HEIRS APPARENT
Buddy explains!
The straight part
We know that "people sure to succeed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case people sure to succeed = heirs apparent.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.