The most common and most likely answer to this crossword clue is the 4 letter word HEIR
I've seen this crossword clue in The Guardian
H
E
I
R
More clues leading to the result HEIR
- Might one succeed with a real burst?
- Legal successor’s manner, so to speak?
- One visiting woman's eldest son perhaps
- Song is heard: one may succeed
- Perhaps first-born's voice heard
- He succeeds with a real criminal
- Charles broadcast to listeners?
- Speaker’s manner, one entitled to succeed
- Next in line on radio broadcast
- Cheekier, disregarding odds, he succeeds
Buddy explains!

The straight part
We know that "Next in line" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case next in line = heir.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 HEIR mean?
HEIR noun- Someone who inherits, or is designated to inherit, the property of another.
- One who inherits, or has been designated to inherit, a hereditary title or office.
- A successor in a role, representing continuity with the predecessor.
- To inherit.